Advanced Linear Algebra - Lecture 2: Subspaces

In this lecture, we learn about vector spaces within vector spaces! Since they're so much easier to work with than vector spaces in general, we give them their own name: subspaces.

Please leave a comment below if you have any questions, comments, or corrections.

Timestamps:
00:00 - Introduction
01:04 - Definition and main theorem
02:40 - Proof
08:28 - Space of polynomials
10:32 - Real symmetric matrices
13:29 - A non-example

[quantabot]

Professor Your delivery is very good, It has speed, accurate and everything is understood. Very impressive, I have been watching many Math channels but never someone deliver like u, its just awesome

[umedina]

The examples are so good! It was hard to me to come with examples were the rules dont hold, but you just pointed it out so clearly. Thanks!!

[quantabot]

I cant wait to have this book, looks amazing

[Miligoran]

Do you know why some textbooks add the property that the zero vector must be an element of the subspace S when it can be shown through the scalar multiplication?

[hearty]

polynomial p(x) and q(x) need not be of same degree, but of course of degree at most p.. so better write p(x)=a_0+a_1x_1+...+a_nx^n and q(x)=b_0+b_1x+...+b_mx^m where, m, n\leq p.

[maxpercer]

your face blocks the bottom of the page 7:50