linear algebra

A collection of 7 posts

Aug 13, 2019

Tensor Products and Multilinear Maps

If you're the sort of person who cowers in fear whenever the word "tensor" is mentioned, this post is for you. We'll pick up right where we left off last time in our discussion of the dual space, and discover how tensor products are a natural extension of the ideas developed in that post.

Aug 8, 2019

Dual Spaces

Since I haven't posted for a while, I decided to break up my rants about homology with some posts on linear (and multilinear) algebra. In this post, we will (as usual) deal only with finite dimensional vector spaces.

Mar 21, 2019

Matrices for Linear Maps

If you already knew some linear algebra before reading my posts, you might be wondering where the heck all the matrices are. The goal of this post is to connect the theory of linear maps and vector spaces to the theory of matrices and computation.

Mar 20, 2019

Linear Maps

Just as we decided to study continuous functions between topological spaces and homomorphisms between groups, much of linear algebra is dedicated to the study of linear maps between vector spaces.

Mar 19, 2019

Bases and Dimension of Vector Spaces

Bases for vector spaces are similar to bases for topological spaces. The idea is that a basis is a small, easy to understand subset of vectors from which it is possible to extrapolate pretty much everything about the vector space as a whole.