Some Results on Combined Matrices

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985807%3A_____%2F17%3A00484984" target="_blank" >RIV/67985807:_____/17:00484984 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.4064/bc112-0-6" target="_blank" >http://dx.doi.org/10.4064/bc112-0-6</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.4064/bc112-0-6" target="_blank" >10.4064/bc112-0-6</a>

Result language
angličtina
Original language name
Some Results on Combined Matrices
Original language description
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.
Czech name
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Czech description
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Project
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2017
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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