Скачать или смотреть LA27 Matrix Multiplication, the How and the Why

How do you multiply #matrices and where does the definition of matrix multiplication come from? Using motivating examples, matrix multiplication is defined. Examples include the input-output tables for a two stage production process and the adjacency matrix of a graph.#linearalgebra #matrixoperations #matrixmultiplication Subscribe ‪@Shahriari‬ for more undergraduate math videos.

00:00 Introduction
00:11 Matrix Vocabulary (   • Видео  )
01:18 Addition & Scalar Multiplication for Matrices
02:06 The dot product of two vectors
02:40 Dot product Example 1: shopping list & prices
03:19 Dot product Example 2: adding votes
03:58 Multiplying a matrix and a vector: Motivating Example
07:50 Multiplying a matrix and a vector: Definition
08:50 Systems of Linear Equations as Matrix Equations
13:10 Multiplying two Matrices: Motivating Example
18:25 Definition of Matrix Multiplication Definition
19:39 Cautionary Tales
23:06 Algebraic Properties of Matrix Multiplication
24:17 A Graph Theory Example: Powers of the Adjacency Matrix (   • CG1 Graphs: Basic Vocabulary  )
Next Video:    • LA28 Matrix Multiplication Revisited; Find...  

This is a video in a series of lectures on linear algebra. The series is a rigorous treatment meant for students with no prior exposure to linear algebra. In this full undergraduate course in linear algebra, general vector spaces and linear transformations are emphasized.

This is also a second lecture in a series of lectures on Matrices and their properties. In later videos, we see that Matrices play an important role in Linear Algebra. We use them in the study of vector spaces and, in return, the theory of vector spaces is used to understand matrices.

Shahriar Shahriari is the William Polk Russell Professor of Mathematics at Pomona College in Claremont, CA USA
Shahriari is a 2015 winner of the Mathematical Association of America's Haimo Award for Distinguished Teaching of Mathematics, and five time winner of Pomona College's Wig teaching award.