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