Hong's canonical form of a Hermitian matrix with respect to orthogonal *congruence
Two matrices \(M\) and \(N\) are orthogonally *congruent if \(S^*MS = N\) for some orthogonal matrix \(S = (S^T)^{-1}\). The main result of this paper is: Theorem. Each Hermitian matrix is orthogonally *congruent to exactly one matrix of the form (1.5) (see the paper), determined up to a permutation of direct summands. The proof uses the fact that two matrices \(M\) and \(N\) are orthogonally *congruent precisely when there exists an orthogonal solution \(X\) of the equation \(M\bar{X} = NX\). The proof is long but easy to follow thanks to two auxiliary lemmas.
scientific article; zbMATH DE number 7403449
scientific article