Скачать или смотреть LA03 R^n (Euclidean n-space), prototypical vector space

The n dimensional Euclidean space (n-space or R^n) is the prototypical example of #vectorspaces Here R^n and vector space properties of the operations of addition and scalar multiplication in R^n are introduced. We also define R^infinity (the vector spaces of infinite sequences), and discuss our motivation for studying abstract vector spaces in #linearalgebra Subscribe ‪@Shahriari‬ for more undergraduate math videos.
00:00 Introduction
00:13 The real numbers R & Operations for R
00:59 R^2, the points on the plane
01:23 The set notation
02:13 Operations for R^2
02:58 R^3 & Operations on R^3
04:02 Why Stop at 3?
04:15 Example: Vote Tallies as elements of R^5
05:48 Definition: R^n or n-space
06:54 Discussion: Row vs Column; order; zero vector
07:46 Addition and Scalar Multiplication in R^n
08:42 Properties of Addition and Scalar Multiplication in R^n
11:38 Definition: Euclidean inner product (dot product)
12:15 Definition: R^infinity and addition and scalar multiplication for sequences
13:16 Discussion: R^n and R^infinity as examples of abstract vector spaces
13:39 Discussion: What is a vector space and why study them?

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.