[[Mathematics MOC]]
# Linear algebra MOC

Linear algebra is the study of [[Category of vector spaces]].
[[Vector notation in these notes]].
Linear algebra is generalized by [[Module theory MOC]].

## Objects

[[Vector space]]

- [[Span]]
- [[Linear (in)dependence]] 
- [[Vector basis]] 
- [[Dimension of a vector space]]

### Extra structure

- [[Quadratic space]]

## Morphisms

- [[Linear map]]

### In a fixed basis

- [[Matrix algebra over a field]] 
- [[Types of square matrix]] 
- [[Row and column space]] 

### Properties of morphisms


- [[Eigenvectors, eigenvalues, and eigenspaces]] 
- [[Diagonalization]]

## Internal constructions

- [[Vector subspace]]
- [[Complement subspace]]

##  Externally

- [[Quotient vector space]]
- [[Direct product vector space]] (product), [[Direct sum of vector spaces]] (coproduct)
- [[Tensor product of vector spaces]]

#
---
#MOC | #state/develop | #SemBr