Topic: Normal Operators and Complex Inner Product Spaces

Proof of Schur’s Triangularization Theorem

Polynomial Functions of Normal Operators

Orthogonality of Eigenspaces of Normal Operators

Normal Operators as Commuting Self-Adjoint Parts

Normal Operators and Their First Examples

Norm Characterizations of Normality

Invariant and Reducing Subspaces of Normal Operators

Inner Product Conventions on Complex Vector Spaces

Existence and Uniqueness of Adjoint Operators

Eigenvalues and Eigenspaces of Unitary Operators