Скачать или смотреть LA05 Matrix Vocabulary & Matrices as Vector Spaces

Basic Matrix Vocabulary is introduced and the set of all n by m #matrices with real entries is given as an example of #vectorspaces Matrix transpose and the trace of a matrix is defined, and is explained why the set of 2x3 matrices with real entries is a six dimensional vector space.#linearalgebra Subscribe ‪@Shahriari‬ for math videos for college students.
00:00 Introduction
00:15 Definition: Matrix, entries, rows and columns
01:12 The Zero matrix
01:22 Square matrices, diagonal of a matrix
01:41 Identity Matrix
02:00 M_{n x m}(R) or R^{n x m} the set of all n x m matrices
02:51 Scalar multiplication for matrices
03:04 Addition of matrices
03:46 Properties of matrix addition and scalar multiplication
05:33 R^{n x m} is a vector space /R
05:47 Basis and dimension for R^{2 x 3}
06:53 F^{n x m} when F is a field is a vector space/F
07:58 Column and row vectors, transpose of a matrix
08:46 Definition: Symmetric Matrix
08:56 Definition: trace of a square matrix

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 series, general vector spaces and linear transformations are emphasized.

In the first few lectures, a number of mathematical structures are studied, and some common features noticed. From these the notion of a vector space is abstracted out. The later lectures will study vector spaces in the abstract.

For an annotated list of available Linear Algebra videos see
https://pomona.box.com/s/oahafa797tj5...
Linear Algebra YouTube Playlist:   • Linear Algebra, a Retro introduction  

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.