Topic: Symmetric Matrices and the Spectral Theorem

Real Eigenvalues of Symmetric Matrices

Real Normal Matrices That Are Not Symmetric

Rayleigh Quotients and Unit-Sphere Geometry

Rank-One Spectral Decomposition

Powers of Symmetric Matrices

Polynomials in a Symmetric Matrix

Orthonormal Bases Within Eigenspaces

Orthogonality of Distinct Eigenspaces

Orthogonal Projectors onto Eigenspaces

Orthogonal Similarity Preserves Symmetry