Скачать или смотреть LA06 Vector Spaces of Functions

Real valued #functions on the real line form a vector space as do the set of functions from any set to a vector space. Function spaces with point wise addition and scalar multiplication are introduced as examples of #vectorspaces The notation R^R for the set of real valued functions on the reals is explained. #linearalgebra Subscribe ‪@Shahriari‬ for in-depth math videos at the college level.
00:00 Introduction
00:11 What is a function? (   • GF1 What is a function? What do 1-1 and on...  )
01:15 Real Valued Functions on the real line, F(R, R) or R^R
02:26 Addition and Scalar Multiplication for Functions
03:29 F(R, R) is a vector space over R
05:26 X any set, then F(X, R) is a vector space over R
05:53 X any set, V vector space over a field F, then F(X, V) is a vector space over F
06:33 F(X, R) = R^X generalizes R^n

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.

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.