Some Results on Combined Matrices

0484984 - ÚI 2018 RIV PL eng C - Conference Paper (international conference)
Fiedler, Miroslav
Some Results on Combined Matrices.
Études opératorielles. Warszawa: Polish Academy of Sciences, 2017 - (Zemánek, J.; Tomilov, Y.), s. 99-105. Banach Center Publications, 112. ISBN 978-83-86806-36-2.
[Conference on Operator Theory and its Applications. Jurata (PL), 18.03.2010-22.03.2010]
Institutional support: RVO:67985807
Keywords : combined matrix * totally nonnegative matrix * oscillatory matrix * Hessenberg CBM-matrix
OECD category: Pure mathematics

A combined matrix of a nonsingular matrix is the Hadamard (entrywise) product of the matrix and its transposed inverse. A characterization of the diagonal entries of the combined matrix of a positive definite matrix was known. In the paper one investigates behaviour of the diagonal entries of combined matrices for some other classes of matrices. In particular, one proves that the diagonal entries of the combined matrix of an oscillatory Hessenberg CBM-matrix are characterized by some four conditions. It leads to the formulation of a conjecture that the first three from these four conditions characterize the diagonal entries of the combined matrix of a square totally positive matrix of arbitrary order. The conjecture is proven for the order equal to 3.
Permanent Link: http://hdl.handle.net/11104/0280113