Скачать или смотреть LA10 An unusual Vector Space

An example of unusual #vectorspaces whose elements are the same as elements of R^2, but the operations of addition and scalar multiplication are not the ordinary operations in R^2. To show that we have a vector space, we work through the definition of a vector space carefully.#linearalgebra
00:00 Introduction
00:12 Definition of a Vector Space (   • LA09 What is a Vector Space? Why study them?  )
01:01 Examples of Vector Spaces (   • LA03 R^n (Euclidean n-space), prototypical...      • LA4 Polynomials, as an example of a vector...      • LA05 Matrix Vocabulary & Matrices as Vecto...  )
01:13 More Examples of Vector Spaces (   • LA06 Vector Spaces of Functions      • LA07 Complex Numbers as a Vector Space and...  )
01:29 An unusual vector space
03:27 Proof: x+y = y +x
04:08 Proof: (x+y)+z = x = (y+z)
04:46 Proof: Existence of the zero vector
05:27 Proof: Existence of additive inverses
06:32 Proof: alpha (x+y) = alpha x + alpha y
07:33 Proof: (alpha + beta)x = alpha x + beta x
08:19 Proof: (alpha beta)x = alpha (beta x)
09:05 Proof: 1x = x
09:25 Motivation behind the example: Frame of Reference

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.

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.