Combined matrices in special classes of matrices

0360426 - ÚI 2012 RIV US eng J - Journal Article
Fiedler, Miroslav - Markham, T. L.
Combined matrices in special classes of matrices.
Linear Algebra and Its Applications. Roč. 435, č. 8 (2011), s. 1945-1955. ISSN 0024-3795. E-ISSN 1873-1856
Institutional research plan: CEZ:AV0Z10300504
Keywords : combined matrix * Hadamard product * positive definite matrix * M-matrix * totally positive matrix * oscillatory matrix * Cauchy matrix
Subject RIV: BA - General Mathematics
Impact factor: 0.974, year: 2011

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.
Permanent Link: http://hdl.handle.net/11104/0197986