Desvl's blog

(Kind of) Missing Content in Your Linear Algebra Class (Still on Progress)

I think it’s quite often that, when you are learning mathematics beyond linear algebra, you are stuck at some linear algebra problems, but you haven’t learnt that systematically before although you wish you had. In this blog post we will go through some content that is not universally taught but quite often used in further mathematics. But this blog post does not serve as a piece of textbook. If you find some interesting topics, you know what document you should read later, and study it later.

This post is still on progress, neither is it finished nor polished properly. For the coming days there will be new contents, untill this line is deleted. What I’m planning to add at this moment:

• Transpose is not just about changing indices of its components.
• Norm and topology in vector spaces
• Representing groups using matrices

Dedekind Domain and Properties in an Elementary Approach

Several ways to prove Hardy's inequality

Tensor Product as a Universal Object (Category Theory & Module Theory)

Why Does a Vector Space Have a Basis (Module Theory)

Rings of Fractions and Localisation

The Grothendienck Group

Study Vector Bundle in a Relatively Harder Way - Tangent Bundle

A Continuous Function Sending L^p Functions to L^1

Study Vector Bundle in a Relatively Harder Way - Definition