LA49 What is a vector space isomorphism?

Can we translate a linear algebra question from one vector space to another, get the answer, and then translate back? We define isomorphisms and isomorphic vector spaces as a way of answering "When are two vector spaces the same?" This motivates the study of linear transformations in subsequent videos. Subscribe @Shahriari for more undergraduate math videos.
00:00 Introduction
01:25 Motivating Question: When are two vector spaces the same?
04:14 Translating from one vector space to another
08:11 Definition: Isomorphism, isomorphic vector spaces
10:16 Example of a vector space isomorphism
12:57 Definition: Linear Transformations, Linear Operators

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.

Shahriar Shahriari is the William Polk Russell Professor of Mathematics at Pomona College in Claremont, CA, U.S.A.