Amitsur's formula, which expresses det(A + B) as a polynomial in coefficients of the characteristic polynomial of a matrix, is generalized for partial linearizations of the pfaffian of block matrices. As applications, in upcoming papers we determine generators for the SO(n)-invariants of several matrices and relations for the O(n)-invariants of several matrices over a field of arbitrary charact...

We propose a new algorithm for the computation of a minimal polynomial basis of the left kernel of a given polynomial matrix F (s): The proposed method exploits the structure of the left null space of generalized Wolovich or Sylvester resultants to compute row polynomial vectors that form a minimal polynomial basis of left kernel of the given polynomial matrix. The entire procedure can be imple...

We extend the algorithm for computing {1}, {1, 3}, {1, 4} inverses and their gradients from [11] to the set of multiple-variable rational and polynomial matrices. An improvement of this extension, appropriate to sparse polynomial matrices with relatively small number of nonzero coefficient matrices as well as in the case when the nonzero coefficient matrices are sparse, is introduced. For that ...

Convolutional codes over rings are particularly suitable for representing codes over phase modulation signals. In order to develop a complete structural analysis of this class of codes, it is necessary to study rational matrices over rings, which constitutes the generator matrices (encoders) for such convolutional codes. Noncatastrophic, minimal, systematic and basic generator matrices are intr...