(ch:la:linear-algebra)=
# Linear Algebra

Primary references for this chapter are 
{cite}`hoffman1971linear,artin2017algebra,aliprantis1998principles`.

Our approach is a mix of traditional algebraic view point of
vector spaces and the analytical view point as our goal is
to quickly review the relevant material as a build-up
towards later chapters.

Chapter objectives:

- Algebraic structures: groups, rings, fields
- Vector spaces
- Span
- Linear independence
- Basis
- Coordinate representation
- Subspaces
- Linear transformation
- Null space / Kernel
- Range  / Image
- Bracket operator
- Matrix representations
- Vector space of linear operators
- Norm
- Normed spaces
- Metric induced by norm
- Inner product
- Inner product spaces
- Norm induced by inner product