Search

The analysis of any Hessenberg matrix as a product of a companion matrix and a triangular matrix is presented in this paper. The factors are explicitly given on terms of the entries of the Hessenberg matrix and, further, various factorizations are undertaken. Applications to comrade and confederate matrices, as well as for the corresponding block cases, are included. [ABSTRACT FROM AUTHOR]

For given m × n matrices G and F over an arbitrary field F , necessary and sufficient conditions (in terms of rank, amongst others) are presented for F to divide G with a square-zero quotient. These results are then used to extend the results of Novak [3] on square-zero factorization to matrices over an arbitrary field. The ranks that the square-zero factors can have are also investigated. Formulae are also presented by which these quotients can be constructed when this type of division is possible. [ABSTRACT FROM AUTHOR]

Abstract: In this paper we present a straightforward proof of the well-known fact that a positive semi-definite polynomial matrix can be written as the product of a polynomial matrix and its associated (Hermitian) transposed. For polynomial matrices with complex coefficients both factors also have complex coefficients and can be taken of the same size as the original matrix. For polynomial matrices with real coefficients both factors may have real coefficients, but then the left factor may need twice as many columns as the original matrix, and analogously for the right factor. [Copyright &y& Elsevier]