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Some results on combined matrices

Volume 112 / 2017

Miroslav Fiedler Banach Center Publications 112 (2017), 99-105 MSC: 15B48; 15A15; 15A23; 15B99. DOI: 10.4064/bc112-0-6

Abstract

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.

Authors

  • Miroslav FiedlerCzech Academy of Sciences
    Institute of Computer Science

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