Hermite normal form and Smith normal form are canonic forms of integral matrices with respect to congruence produced by multiplication with right unimodular matrix resp. by multiplication with left and right unimodular matrix simultaneously. This lower-diagonal resp. diagonal form has many applications in various elds. Unfortunately, the computation of them is extremely resource consuming. The ...

A pair of matrices is said to be imbeddable precisely when one is an isometric projection of the other on a suitable subspace. The concept of imbedding has been the subject of extensive study. Particular emphasis has been placed on relating the spectra of the matrices involved, especially when both matrices are Hermitian or normal. In this paper, the notion of block imbedding is introduced and ...

Canonical forms are developed for several sets of matrices that are normal with respect to an indefinite inner product induced by a nonsingular Hermitian, symmetric, or skewsymmetric matrix. The most general result covers the case of polynomially normal matrices, i.e., matrices whose adjoint with respect to the indefinite inner product is a polynomial of the original matrix. From this result, c...

Canonical forms are developed for several sets of matrices that are normal with respect to an indefinite inner product induced by a nonsingular Hermitian, symmetric, or skewsymmetric matrix. The most general result covers the case of polynomially normal matrices, i.e., matrices whose adjoint with respect to the indefinite inner product is a polynomial of the original matrix. From this result, c...

In this article, we prove a class of normal dilation matrices affirming the Marcus-de Oliveira conjecture.

In this note, analytic description of V 3 (A) is given for normal matrices of the form A = A 1 ⊕ iA 2 or A = A 1 ⊕ e i 2π 3 A 2 ⊕ e i 4π 3 A 3 , where A 1 , A 2 , A 3 are Hermitian matrices. The new concept " k th roots of a convex set " is used to study the polynomial numerical hulls of order k for normal matrices.