Search results “Matrix multiplication dot product”

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MathTheBeautiful

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mathbff

Definitions of the vector dot product and vector length
Watch the next lesson: https://www.khanacademy.org/math/linear-algebra/vectors_and_spaces/dot_cross_products/v/proving-vector-dot-product-properties?utm_source=YT&utm_medium=Desc&utm_campaign=LinearAlgebra
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Linear Algebra on Khan Academy: Have you ever wondered what the difference is between speed and velocity? Ever try to visualize in four dimensions or six or seven? Linear algebra describes things in two dimensions, but many of the concepts can be extended into three, four or more. Linear algebra implies two dimensional reasoning, however, the concepts covered in linear algebra provide the basis for multi-dimensional representations of mathematical reasoning. Matrices, vectors, vector spaces, transformations, eigenvectors/values all help us to visualize and understand multi dimensional concepts. This is an advanced course normally taken by science or engineering majors after taking at least two semesters of calculus (although calculus really isn't a prereq) so don't confuse this with regular high school algebra.
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Khan Academy

University of Hawaii, Dept. of Geology & Geophysics, Garrett Apuzen-Ito, GG413: Geological Data Analysis
www.soest.hawaii.edu/GG/FACULTY/ITO/GG413

Views: 2153
Garrett Apuzen-Ito

Views: 5586
Vidya Sagar

Defining and understanding what it means to take the product of a matrix and a vector
Watch the next lesson: https://www.khanacademy.org/math/linear-algebra/vectors_and_spaces/null_column_space/v/introduction-to-the-null-space-of-a-matrix?utm_source=YT&utm_medium=Desc&utm_campaign=LinearAlgebra
Missed the previous lesson?
https://www.khanacademy.org/math/linear-algebra/vectors_and_spaces/matrices_elimination/v/matrices-reduced-row-echelon-form-3?utm_source=YT&utm_medium=Desc&utm_campaign=LinearAlgebra
Linear Algebra on Khan Academy: Have you ever wondered what the difference is between speed and velocity? Ever try to visualize in four dimensions or six or seven? Linear algebra describes things in two dimensions, but many of the concepts can be extended into three, four or more. Linear algebra implies two dimensional reasoning, however, the concepts covered in linear algebra provide the basis for multi-dimensional representations of mathematical reasoning. Matrices, vectors, vector spaces, transformations, eigenvectors/values all help us to visualize and understand multi dimensional concepts. This is an advanced course normally taken by science or engineering majors after taking at least two semesters of calculus (although calculus really isn't a prereq) so don't confuse this with regular high school algebra.
About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.
For free. For everyone. Forever. #YouCanLearnAnything
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Khan Academy

Thanks to all of you who support me on Patreon. You da real mvps! $1 per month helps!! :) https://www.patreon.com/patrickjmt !! For more FREE math videos, visit http://PatrickJMT.com !!
Vectors - The Dot Product. I show how to compute the dot product of two vectors, along with some useful theorems and results involving dot products. 3 complete examples are shown.

Views: 834815
patrickJMT

Introduction to the vector dot product. Created by Sal Khan.
Watch the next lesson: https://www.khanacademy.org/science/physics/magnetic-forces-and-magnetic-fields/electric-motors/v/dot-vs-cross-product?utm_source=YT&utm_medium=Desc&utm_campaign=physics
Missed the previous lesson? https://www.khanacademy.org/science/physics/magnetic-forces-and-magnetic-fields/electric-motors/v/magnetism-11-electric-motors?utm_source=YT&utm_medium=Desc&utm_campaign=physics
Physics on Khan Academy: Physics is the study of the basic principles that govern the physical world around us. We'll start by looking at motion itself. Then, we'll learn about forces, momentum, energy, and other concepts in lots of different physical situations. To get the most out of physics, you'll need a solid understanding of algebra and a basic understanding of trigonometry.
About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.
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Khan Academy

Dot products are a nice geometric tool for understanding projection. But now that we know about linear transformations, we can get a deeper feel for what's going on with the dot product, and the connection between its numerical computation and its geometric interpretation.
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3blue1brown is a channel about animating math, in all senses of the word animate. And you know the drill with YouTube, if you want to stay posted about new videos, subscribe, and click the bell to receive notifications (if you're into that).
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3Blue1Brown

Visual interpretation of the cross product and the dot product of two vectors.
My Patreon page: https://www.patreon.com/EugeneK

Views: 364015
Physics Videos by Eugene Khutoryansky

This physics video tutorial explains how to find the cross product of two vectors using matrices and determinants and how to confirm your answer using the dot product formula. This video contains plenty of examples and practice problems using the components i j k.

Views: 30573
The Organic Chemistry Tutor

Interpretations of A.B in terms of dot products of rows of A with columns of B, A with columns of B, rows of A with B, row matrices of A with column matrices of B, sum of outer products of columns of A with corresponding rows of B. AX, X a vector, is the linear combination of columns of A with weights same as entries of vector X.

Views: 85
online math

Multiplying matrices example explained step by step. http://MathMeeting.com

Views: 588722
Math Meeting

Practice this lesson yourself on KhanAcademy.org right now:
https://www.khanacademy.org/math/precalculus/precalc-matrices/Basic_matrix_operations/e/scalar_matrix_multiplication?utm_source=YT&utm_medium=Desc&utm_campaign=Precalculus
Watch the next lesson: https://www.khanacademy.org/math/precalculus/precalc-matrices/Basic_matrix_operations/v/matrix-addition-and-subtraction-1?utm_source=YT&utm_medium=Desc&utm_campaign=Precalculus
Missed the previous lesson?
https://www.khanacademy.org/math/precalculus/precalc-matrices/Basic_matrix_operations/v/data-in-matrices?utm_source=YT&utm_medium=Desc&utm_campaign=Precalculus
Precalculus on Khan Academy: You may think that precalculus is simply the course you take before calculus. You would be right, of course, but that definition doesn't mean anything unless you have some knowledge of what calculus is. Let's keep it simple, shall we? Calculus is a conceptual framework which provides systematic techniques for solving problems. These problems are appropriately applicable to analytic geometry and algebra. Therefore....precalculus gives you the background for the mathematical concepts, problems, issues and techniques that appear in calculus, including trigonometry, functions, complex numbers, vectors, matrices, and others. There you have it ladies and gentlemen....an introduction to precalculus!
About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.
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Views: 386658
Khan Academy

Testing out this animation tool I'm making https://github.com/JonComo/anim
Starting with smaller videos, ultimately working my way towards a series on neural networks, so stick around for that! I'm going to cover everything assuming no background knowledge. It's going to be a lot to cover but I'm excited to go through it step by step and make it as understandable as I can.

Views: 3514
giant_neural_network

Writing the Euclidean inner product in the form of matrix multiplication.

Views: 1503
Juan Klopper

compute the product of 3x3 matrices dot product of two matrices how to multiply 3x3 matrices

Views: 9179
Ncert Solutions CBSE ncerthelp.com

3.4.1 Matrix-vector multiplication via dot product

This video is about Linear Algebra: Matrix Multiplication and the Dot Product of a Vector

Views: 246
Eva Loveland

how to multiply matrices is a que in mind of students.this is very simple method for begineers.
Matrices and Determinants in Most imp. Chapter for class 12 .
Matrix multiplication: Very Simple Method
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Mandhan Academy

I hadn't seen that matrix multiplies are really just dot products until last week.

Views: 4066
Hamilton Carter

This is video number 3 in the Linear Algebra series by Free Academy

Views: 120
Free Academy for Math

Multiplying two 2x2 matrices.
Practice this yourself on Khan Academy right now: https://www.khanacademy.org/e/multiplying_a_matrix_by_a_matrix?utm_source=YTdescription&utm_medium=YTdescription&utm_campaign=YTdescription

Views: 1057326
Khan Academy

Practice this lesson yourself on KhanAcademy.org right now:
https://www.khanacademy.org/math/precalculus/precalc-matrices/matrix_multiplication/e/multiplying_a_matrix_by_a_vector?utm_source=YT&utm_medium=Desc&utm_campaign=Precalculus
Watch the next lesson: https://www.khanacademy.org/math/precalculus/precalc-matrices/matrix_multiplication/v/defined-and-undefined-matrix-operations?utm_source=YT&utm_medium=Desc&utm_campaign=Precalculus
Missed the previous lesson?
https://www.khanacademy.org/math/precalculus/precalc-matrices/matrix_multiplication/v/multiplying-a-matrix-by-a-matrix?utm_source=YT&utm_medium=Desc&utm_campaign=Precalculus
Precalculus on Khan Academy: You may think that precalculus is simply the course you take before calculus. You would be right, of course, but that definition doesn't mean anything unless you have some knowledge of what calculus is. Let's keep it simple, shall we? Calculus is a conceptual framework which provides systematic techniques for solving problems. These problems are appropriately applicable to analytic geometry and algebra. Therefore....precalculus gives you the background for the mathematical concepts, problems, issues and techniques that appear in calculus, including trigonometry, functions, complex numbers, vectors, matrices, and others. There you have it ladies and gentlemen....an introduction to precalculus!
About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.
For free. For everyone. Forever. #YouCanLearnAnything
Subscribe to Khan Academy’s Precalculus channel:
https://www.youtube.com/channel/UCBeHztHRWuVvnlwm20u2hNA?sub_confirmation=1
Subscribe to Khan Academy: https://www.youtube.com/subscription_center?add_user=khanacademy

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Khan Academy

Interpretations of A.B in terms of dot products of rows of A with columns of B, A with columns of B, rows of A with B, row matrices of A with column matrices of B, sum of outer products of columns of A with corresponding rows of B. AX, X a vector, is the linear combination of columns of A with weights same as entries of vector X.

Views: 134
Omnia A

The definition of the dot product and its relation to matrix multiplication.

Views: 276
Jason Rose

This video will show you how to multiply two matrices using your Casio Fx-991ES Plus. To access the matrix mode press mode 6. As always to return your calculator to normal press mode 1.

Views: 268397
Calculator Expert

In this video, I go through an easy to follow example that teaches you how to perform Boolean Multiplication on matrices. This makes a confusing process easy. Feel free to comment with any remaining questions you still have, and of course I'm always open to feedback and suggested topics.
Have an integreat day!

Views: 16881
MathHacks

Check us out at http://math.tutorvista.com/algebra/matrix-multiplication.html
Matrix Multiplication
The ordinary matrix product is the most often used and the most important way to multiply matrices. It is defined between two matrices only if the width of the first matrix equals the height of the second matrix. Multiplying an m×n matrix with an n×p matrix results in an m×p matrix. If many matrices are multiplied together, and their dimensions are written in a list in order, e.g. m×n, n×p, p×q, q×r, the size of the result is given by the first and the last numbers (m×r), and the values surrounding each comma must match for the result to be defined. The ordinary matrix product is not commutative.
The element x3,4 of the above matrix product is computed as follows
The first coordinate in matrix notation denotes the row and the second the column; this order is used both in indexing and in giving the dimensions. The element at the intersection of row i and column j of the product matrix is the dot product (or scalar product) of row i of the first matrix and column j of the second matrix. This explains why the width and the height of the matrices being multiplied must match: otherwise the dot product is not defined.
The figure to the right illustrates the product of two matrices A and B, showing how each intersection in the product matrix corresponds to a row of A and a column of B. The size of the output matrix is always the largest possible, i.e. for each row of A and for each column of B there are always corresponding intersections in the product matrix. The product matrix AB consists of all combinations of dot products of rows of A and columns of B.
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TutorVista

For Guidance Contact : [email protected]

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Anil Kumar

Learn Neural Net Programming: http://www.heatonresearch.com/course/intro-neural-nets-cs
In class session 2, part 4 we will look at matrix operations that are important to neural networks. We will see matrix multiplication, dot product, as well as matrix addition and subtraction.

Views: 11505
Jeff Heaton

Multiplying two matrices represents applying one transformation after another. Many facts about matrix multiplication become much clearer once you digest this fact.
Full series: http://3b1b.co/eola
Future series like this are funded by the community, through Patreon, where supporters get early access as the series is being produced.
http://3b1b.co/support
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3blue1brown is a channel about animating math, in all senses of the word animate. And you know the drill with YouTube, if you want to stay posted about new videos, subscribe, and click the bell to receive notifications (if you're into that).
If you are new to this channel and want to see more, a good place to start is this playlist: https://goo.gl/WmnCQZ
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Views: 600380
3Blue1Brown

Matrix Multiplication - Learn how to multiply matrix and matrix rules of multiplication of two matrix and more matrices.
Learn multiplying a matrix by anothe martix, with help of dot product or cross product of rows and columns and find product martix.
Don't forget to subscribe us for more Math in Hindi videos.

Views: 604
Skill Ark

kobriendublin.wordpress.com
Matrix multiplication of two square matrices A and B.

Views: 4521
Dragonfly Statistics

Thanks to all of you who support me on Patreon. You da real mvps! $1 per month helps!! :) https://www.patreon.com/patrickjmt !! In this video, I give the formula for the cross product of two vectors, discuss geometrically what the cross product is, and do an example of finding the cross product.
For more free math videos, visit http://PatrickJMT.com

Views: 705500
patrickJMT

In this presentation we shall review the different properties of vector operations in 3D and also solve some example problems.

Views: 2528
Ram Polepeddi

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Telusko

Matrices shortcuts and tricks
Multiplication of matrices
tricks to multiply matrices
matrix multiplication
Class 11 matrices
class 12 matrices
Matrices multiplication inverse 3x3 2x2 3x2
Unit II: Algebra
1. Matrices
Concept, notation, order, equality, types of matrices, zero and identity matrix, transpose of a matrix, symmetric and skew symmetric matrices. Operation on matrices: Addition and multiplication and multiplication with a scalar. Simple properties of addition, multiplication and scalar multiplication. Noncommutativity of multiplication of matrices and existence of non-zero matrices whose product is the zero matrix (restrict to square matrices of order 2).Concept of elementary row and column operations. Invertible matrices and proof of the uniqueness of inverse, if it exists;
2. Determinants
Determinant of a square matrix (up to 3 x 3 matrices), properties of determinants, minors, co-factors and applications of determinants in finding the area of a triangle. Adjoint and inverse of a square matrix. Consistency, inconsistency and number of solutions of system of linear equations by examples, solving system of linear equations in two or three variables (having unique solution) using inverse of a matrix.
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Mandhan Academy

► My Precalculus course: https://www.kristakingmath.com/precalculus-course
In this video we’re talking about everything you need to know about matrix multiplication. We’ll start simple and look at what it means to multiply a matrix by a scalar, and then move on to multiplying matrices together using the dot product, and a special trick for remembering how to do matrix multiplication.
We’ll cover rules of algebra for matrices, including commutative, associative, and distributive properties, and show that each of these properties applies to matrix multiplication, except for the commutative property.
We’ll talk about matrix dimensions and how to describe a matrix by its rows and columns. We’ll address the fact that not all matrix multiplication is defined, and that you in fact need the number of columns in the first matrix to match the number of rows in the second matrix in order for the multiplication to work at all. You can also use matrix dimensions to figure out the dimensions of the resulting matrix after the multiplication.
Finally, we’ll look at identity matrices and zero matrices, which act like the special numbers 1 and 0 when it comes to matrix multiplication.
0:17 // Multiplying a matrix by a scalar
0:37 // Applying algebra to matrices
0:44 // Matrix multiplication is not commutative
1:21 // Associative property and distributive property with matrices
2:00 // Matrix dimensions
2:21 // Which matrices can be multiplied together?
2:55 // How to figure out whether matrices can be multiplied together. How to figure out the dimensions of the resulting matrix.
3:40 // How to multiply matrices using the dot product
4:26 // How to remember what to put where
5:16 // Identity matrices
5:51 // Multiplying by the identity matrix is like multiplying by 1
6:31 // Multiplicative inverses
6:56 // Zero matrices
7:23 // Summary
Music by Joakim Karud: http://soundcloud.com/joakimkarud
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Math class was always so frustrating for me. I’d go to a class, spend hours on homework, and three days later have an “Ah-ha!” moment about how the problems worked that could have slashed my homework time in half. I’d think, “WHY didn’t my teacher just tell me this in the first place?!”
So I started tutoring to keep other people out of the same aggravating, time-sucking cycle. Since then, I’ve recorded tons of videos and written out cheat-sheet style notes and formula sheets to help every math student—from basic middle school classes to advanced college calculus—figure out what’s going on, understand the important concepts, and pass their classes, once and for all. Interested in getting help? Learn more here: http://www.kristakingmath.com
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Views: 8737
Krista King

This course is on Lemma: http://lem.ma Lemma looking for developers: http://lem.ma/jobs
Other than http://lem.ma, I recommend Strang http://bit.ly/StrangYT, Gelfand http://bit.ly/GelfandYT, and my short book of essays http://bit.ly/HALAYT
Questions and comments below will be promptly addressed.
Linear Algebra is one of the most important subjects in mathematics. It is a subject with boundless practical and conceptual applications.
Linear Algebra is the fabric by which the worlds of geometry and algebra are united at the most profound level and through which these two mathematical worlds make each other far more powerful than they ever were individually.
Virtually all subsequent subjects, including applied mathematics, physics, and all forms of engineering, are deeply rooted in Linear Algebra and cannot be understood without a thorough understanding of Linear Algebra. Linear Algebra provides the framework and the language for expressing the most fundamental relationships in virtually all subjects.
This collection of videos is meant as a stand along self-contained course. There are no prerequisites. Our focus is on depth, understanding and applications. Our innovative approach emphasizes the geometric and algorithmic perspective and was designed to be fun and accessible for learners of all levels.
Numerous exercises will be provided via the Lemma system (under development)
We will cover the following topics:
Vectors
Linear combinations
Decomposition
Linear independence
Null space
Span
Linear systems
Gaussian elimination
Matrix multiplication and matrix algebra
The inverse of a matrix
Elementary matrices
LU decomposition
LDU decomposition
Linear transformations
Determinants
Cofactors
Eigenvalues
Eigenvectors
Eigenvalue decomposition (also known as the spectral decomposition)
Inner product (also known as the scalar product and dot product)
Self-adjoint matrices
Symmetric matrices
Positive definite matrices
Cholesky decomposition
Gram-Schmidt orthogonalization
QR decomposition
Elements of numerical linear algebra
I’m Pavel Grinfeld. I’m an applied mathematician. I study problems in differential geometry, particularly with moving surfaces.

Views: 3156
MathTheBeautiful

This lesson discusses the notations involved with the dot product, and the notation that is involved with the inner product. We will go more in depth in the actual book.

Views: 4961
JJtheTutor

We can use indices to write matrix multiplication in a more compact way.

Views: 10332
PhysicsHelps

Taking the transpose of the product of two matrices
Watch the next lesson: https://www.khanacademy.org/math/linear-algebra/matrix_transformations/matrix_transpose/v/linear-algebra-transposes-of-sums-and-inverses?utm_source=YT&utm_medium=Desc&utm_campaign=LinearAlgebra
Missed the previous lesson?
https://www.khanacademy.org/math/linear-algebra/matrix_transformations/matrix_transpose/v/linear-algebra-determinant-of-transpose?utm_source=YT&utm_medium=Desc&utm_campaign=LinearAlgebra
Linear Algebra on Khan Academy: Have you ever wondered what the difference is between speed and velocity? Ever try to visualize in four dimensions or six or seven? Linear algebra describes things in two dimensions, but many of the concepts can be extended into three, four or more. Linear algebra implies two dimensional reasoning, however, the concepts covered in linear algebra provide the basis for multi-dimensional representations of mathematical reasoning. Matrices, vectors, vector spaces, transformations, eigenvectors/values all help us to visualize and understand multi dimensional concepts. This is an advanced course normally taken by science or engineering majors after taking at least two semesters of calculus (although calculus really isn't a prereq) so don't confuse this with regular high school algebra.
About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.
For free. For everyone. Forever. #YouCanLearnAnything
Subscribe to KhanAcademy’s Linear Algebra channel:: https://www.youtube.com/channel/UCGYSKl6e3HM0PP7QR35Crug?sub_confirmation=1
Subscribe to KhanAcademy: https://www.youtube.com/subscription_center?add_user=khanacademy

Views: 64811
Khan Academy

scalar matrix multiplication & its example
hit that like button and subscribe my channel for more videos :)

Views: 2513
Online Class

Multiplication Of Matrices
In mathematics, matrix multiplication is the operation of multiplying a matrix with either a scalar or another matrix. This article gives an overview of the various types of matrix multiplication.
he ordinary matrix product is the most often used and the most important way to multiply matrices. It is defined between two matrices only if the width of the first matrix equals the height of the second matrix. Multiplying an m×n matrix with an n×p matrix results in an m×p matrix. If many matrices are multiplied together, and their dimensions are written in a list in order, e.g. m×n, n×p, p×q, q×r, the size of the result is given by the first and the last numbers (m×r), and the values surrounding each comma must match for the result to be defined. The ordinary matrix product is not commutative.
The element x3,4 of the above matrix product is computed as follows
The first coordinate in matrix notation denotes the row and the second the column; this order is used both in indexing and in giving the dimensions. The element at the intersection of row i and column j of the product matrix is the dot product (or scalar product) of row i of the first matrix and column j of the second matrix. This explains why the width and the height of the matrices being multiplied must match: otherwise the dot product is not defined.
The figure to the right illustrates the product of two matrices A and B, showing how each intersection in the product matrix corresponds to a row of A and a column of B. The size of the output matrix is always the largest possible, i.e. for each row of A and for each column of B there are always corresponding intersections in the product matrix. The product matrix AB consists of all combinations of dot products of rows of A and columns of B.
Checkout for more information: https://math.tutorvista.com/algebra/matrices.html
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Views: 6552
TutorVista

This course is on Lemma: http://lem.ma Lemma looking for developers: http://lem.ma/jobs
Other than http://lem.ma, I recommend Strang http://bit.ly/StrangYT, Gelfand http://bit.ly/GelfandYT, and my short book of essays http://bit.ly/HALAYT
Questions and comments below will be promptly addressed.
Linear Algebra is one of the most important subjects in mathematics. It is a subject with boundless practical and conceptual applications.
Linear Algebra is the fabric by which the worlds of geometry and algebra are united at the most profound level and through which these two mathematical worlds make each other far more powerful than they ever were individually.
Virtually all subsequent subjects, including applied mathematics, physics, and all forms of engineering, are deeply rooted in Linear Algebra and cannot be understood without a thorough understanding of Linear Algebra. Linear Algebra provides the framework and the language for expressing the most fundamental relationships in virtually all subjects.
This collection of videos is meant as a stand along self-contained course. There are no prerequisites. Our focus is on depth, understanding and applications. Our innovative approach emphasizes the geometric and algorithmic perspective and was designed to be fun and accessible for learners of all levels.
Numerous exercises will be provided via the Lemma system (under development)
We will cover the following topics:
Vectors
Linear combinations
Decomposition
Linear independence
Null space
Span
Linear systems
Gaussian elimination
Matrix multiplication and matrix algebra
The inverse of a matrix
Elementary matrices
LU decomposition
LDU decomposition
Linear transformations
Determinants
Cofactors
Eigenvalues
Eigenvectors
Eigenvalue decomposition (also known as the spectral decomposition)
Inner product (also known as the scalar product and dot product)
Self-adjoint matrices
Symmetric matrices
Positive definite matrices
Cholesky decomposition
Gram-Schmidt orthogonalization
QR decomposition
Elements of numerical linear algebra
I’m Pavel Grinfeld. I’m an applied mathematician. I study problems in differential geometry, particularly with moving surfaces.

Views: 3126
MathTheBeautiful

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After the good princess had breathed her last and had been honorably buried, Tebaldo indulged in the thought of wedding again, but he bore well in mind the promise he had made to his wife, and was firmly resolved to keep her saying. However, the report that Tebaldo, Prince of Salerno, was seeking another mate soon got noised abroad, and came to the ears of many maidens who, in worth and in estate, were no whit his inferiors; but Tebaldo, whose first care was to fulfil the wishes of his wife who was dead, made it a condition that any damsel who might be offered to him in marriage should first try on her finger his wifes ring, to see whether it fitted, and not having found one who fulfilled this condition -- the ring being always found too big for this and too small for that -- he was forced to dismiss them all without further parley. Now it happened one day that the daughter of Tebaldo, whose name was Doralice, sat at table with her father; and she, having espied her mothers ring lying on the board, slipped it on her finger and cried out, "See my father, how well my mothers ring fits me!" And the prince, when he saw what she had done, assented. But not long after this the soul of Tebaldo was assailed by a strange and diabolical temptation to take to wife his daughter Doralice, and for many days he lived tossed about between yea and nay. At last, overcome by the strength of this devilish intent, and fired by the beauty of the maiden, he one day called her to him and said, "Doralice, my daughter, while your mother was yet alive, but fast nearing the end of her days, she besought me never to take to wife any woman whose finger would not fit the ring she herself always wore in her lifetime, and I swore by my head that I would observe this last request of hers. Wherefore, when I felt the time was come for me to wed anew, I made trial of many maidens, but not one could I find who could wear your mothers ring, except yourself. Therefore I have decided to take you for my wife, for thus I shall satisfy my own desire without violating the promise I made to your mother." Doralice, who was as pure as she was beautiful, when she listened to the evil designs of her wicked father, was deeply troubled in her heart; but, taking heed of his vile and abominable lust, and fearing the effects of his rage, she made no answer and went out of his presence with an untroubled face. As there was no one whom she could trust so well as her old nurse, she repaired to her at once as the surest bulwark of her safety, to take counsel as to what she should do. The nurse, when she had heard the story of the execrable lust of this wicked father, spake words of comfort to Doralice, for she knew well the constancy and steadfast nature of the girl, and that she would be ready to endure any torment rather than accede to her fathers desire, and promised to aid her in keeping her virginity unsullied by such terrible disgrace.