Normal Operators

Change of Variables in Integration in R^n

Determinant of an Operator and of a Matrix

Trace of an Operator and of a Matrix

Change of Basis

Isometries on Real Inner Product Spaces

Normal Operators on Real Inner Product Spaces

Complexification

Jordan Form

The Minimal Polynomial

The Characteristic Polynomial

Square Roots of Operators

Block Diagonal Matrices

Decomposition Via Generalized Eigenvectors

Nilpotent Operators

Generalized Eigenvectors

Null Spaces of Powers of an Operator

Singular Value Decomposition

Polar Decomposition

Isometries

Positive Operators

The Spectral Theorem

Normal Operators

Self-Adjoint Operators

Adjoints