Topic: Normal Operators and Complex Inner Product Spaces

Why a Normal Triangular Matrix Is Diagonal

Unitary Operators and Inner-Product Preservation

Unitary Diagonalization Criteria for Complex Matrices

Two-by-Two Complex Normal Matrices

The Matrix Formula for an Adjoint

The Discrete Fourier Matrix as a Unitary Operator

Spectral Projections of a Normal Operator

Self-Adjoint Operators and Real Eigenvalues

Schur Triangularization and Its Matrix Form

Proof of the Complex Spectral Theorem