Canonical forms for normal matrices that commute with their complex conjugate

Roots and Canonical Forms for Circulant Matrices

Matrices that commute with their derivative . On a letter from Schur to Wielandt . † Olga Holtz

We examine when a matrix whose elements are differentiable functions in one variable commutes with its derivative. This problem was discussed in a letter from Issai Schur to Helmut Wielandt written in 1934, which we found in Wielandt’s Nachlass. We present this letter and its translation into English. The topic was rediscovered later and partial results were proved. However, there are many subt...

Canonical matrices of bilinear and sesquilinear forms

Canonical matrices are given for • bilinear forms over an algebraically closed or real closed field; • sesquilinear forms over an algebraically closed field and over real quaternions with any nonidentity involution; and • sesquilinear forms over a field F of characteristic different from 2 with involution (possibly, the identity) up to classification of Hermitian forms over finite extensions of...

Normal forms for general polynomial matrices

We present an algorithm for the computation of a shifted Popov Normal Form of a rectangular polynomial matrix. For specific input shifts, we obtain methods for computing the matrix greatest common divisor of two matrix polynomials (in normal form) or such polynomial normal form computation as the classical Popov form and the Hermite Normal Form. The method is done by embedding the problem of co...

Canonical forms for doubly structured matrices and pencils

In this paper we derive canonical forms under structure preserving equivalence transformations for matrices and matrix pencils that have a multiple structure, which is either an H-selfadjoint or H-skew-adjoint structure, where the matrix H is a complex nonsingular Hermitian or skew-Hermitian matrix. Matrices and pencils of such multiple structures arise for example in quantum chemistry in Hartr...