A generalization of Sylvesterʹs law of inertia Original Research Article

We introduce the class of unitoid matrices as those that are diagonalizable by congruence; the nondegenerate canonical angles of a unitoid matrix A are the directions of the nonzero entries of a diagonal matrix congruent to A (which are shown to be unique). Sylvesterʹs law states that two Hermitian matrices of the same size are congruent if and only if they have the same numbers of positive (respectively, negative) eigenvalues. Two unitoid matrices are congruent if and only if they have the same nondegenerate canonical angles.