Combined matrices in special classes of matrices

Authors: Miroslav Fiedler, T. L. Markham
Publication year: 2011
Publication type: Článek v odborném periodiku
Periodical: Linear Algebra and Its Applications
Bibliographic citation: FIEDLER, Miroslav, MARKHAM, T. L. Combined matrices in special classes of matrices. Linear Algebra and Its Applications. 2011, 435(8), 1945-1955. ISSN 0024-3795. E-ISSN 1873-1856
Dostupné z: doi:10.1016/j.laa.2011.03.054
DOI: 10.1016/j.laa.2011.03.054
ID: 360426

Abstract

The combined matrix of a nonsingular matrix A is the matrix A o (A(-1))(T), where o means the Hadamard (entrywise) product. It has simple properties, its row- as well as column-sums are always one, and it is not changed if A is multiplied from either side by a nonsingular diagonal matrix. Although it is usually difficult to compute, its further properties deserve attention. In the paper, we concentrate on the sequence of the diagonal entries of combined matrices in various classes of matrices.