Diagonalization Similar matrices. The characteristic polynomial, characteristic equation, eigenvalues, and trace of a square matrix. Eigenvalues and eigenvectors for endomorphisms. Diagonalizable square matrices. How to calculate powers of a diagonalizable matrix A. Chapter 6.
Inner product spaces Inner products and inner product spaces.
Orthogonality of vectors. The Hermitian adjoint of a square matrix. Orthogonal bases and orthonormal bases for finite-dimensional subspaces of an inner product space. The Gram-Schmidt process. The following books are all worth looking at.