A Second Course in Linear Algebra » Reference » Proof Techniques »
Proof Techniques

A Second Course in Linear Algebra

  • Preface
  • Dedication and Acknowledgements

Canonical Forms

  • Nilpotent Linear Transformations
  • Invariant Subspaces
  • Jordan Canonical Form

Matrix Decompositions

  • Rank One Decomposition
  • Triangular Decomposition
  • Singular Value Decomposition
  • Square Roots
  • Polar Decomposition

Topics

  • Fields
  • Trace
  • Hadamard Product
  • Vandermonde Matrix
  • Positive Semi-Definite Matrices

Applications

  • Curve Fitting
  • Sharing a Secret

Archetypes

  •   ABCDEFGHIJKLM
  •   NOPQRSTUVWX

Reference

  • Notation
  • Definitions
  • Theorems
  • Examples
  • Sage
  • Proof Techniques
  • GFDL License