We obtain a new bound in the uniform version of Glasner property for matrices with polynomial entries, improving that K. Bulinski and A. Fish (2021). This improvement is based on more careful examination complete rational exponential sums polynomials can perhaps be used other questions similar spirit.

In this paper a new family of companion forms associated to a regular polynomial matrix is presented. Similar results have been presented in a recent paper by M. Fiedler, where the scalar case is considered. It is shown that the new family of companion forms preserves both the finite and infinite elementary divisors structure of the original polynomial matrix, thus all its members can be seen a...

We rst review the basic properties of the well known classes of Toeplitz Hankel Vandermonde and other related structured matrices and re examine their correlation to operations with univariate polynomials Then we de ne some natural extensions of such classes of matrices based on their correlation to multivariate polynomials We describe the correlation in terms of the associated operators of mul...

Matrix polynomials appear in many areas of computational algebra, control systems theory, di‚erential equations, and mechanics, typically with real or complex coecients. Because of numerical error and instability, a matrix polynomial may appear of considerably higher rank (generically full rank), while being very close to a rank-de€cient matrix. “Close” is de€ned naturally under the Frobenius ...