4. Linear Algebra#

Primary references for this chapter are [1, 2, 16].

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