LA09 What is a Vector Space? Why study them?

Abstract #vectorspaces over the reals are defined, and examples are given. R^n, #polynomials, #matrices , real valued functions, and #complexnumbers are given as examples. The project of studying abstract vector spaces as well as #fields and scalars other than reals are discussed.#linearalgebra Subscribe @Shahriari for in-dept math videos for college students.
00:00 Introduction
02:21 What is a Vector Space?
03:38 Axioms for addition & scalar multiplication in Vector Spaces
05:24 Definition: Vector Space
07:48 What is a Vector?
08:18 Why study abstract vector spaces?
10:21 How to study vector spaces?
10:49 Role of Proofs
11:30 When scalars aren't real numbers

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

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.