Normal matrices for physicists

Abstract

Normal matrices are the largest class of matrices which can be diagonalized by unitary transformations. They include Hermitian, anti-Hermitian, unitary, real symmetric, and real orthogonal matrices, the primary types of interest to physicists. An aesthetically and practically satisfying synthesis as well as a significant saving of effort is achieved by studying normal matrices first and then deducing results for the various particular types subsequently. A simple constructive proof of the fundamental result that every normal matrix can be diagonalized by a unitary matrix is given.