Linear algebra

Vector spaces

TBD

A vector space over a field \(\mathbb{F}\) is a set \(V\) along with two operations:

1. \(+: V \times V \to V\) (vector addition)
2. \(\cdot: \mathbb{F} \times V \to V\) (scalar multiplication)

that satisfies the following properties:

1. TBD

We call the elements of \(V\) vectors and the elements of \(\mathbb{F}\) scalars.

Dimensions and bases

TBD

Linear transformations

TBD

Eigenvalues and eigenvectors

TBD

Matrix decompositions

TBD

Matrix stacking

TBD