The polynomial identities for matrix functions
Georgy P. Egorychev
TL;DR
This paper reviews recent advances in deriving polynomial identities for matrix functions, including noncommutative cases and determinants, using polarization theorems, highlighting new computational formulas and theoretical insights.
Contribution
The paper presents new polynomial identities for matrix functions, extending polarization techniques to noncommutative variables and determinants of space matrices.
Findings
Derived polynomial identities for matrix functions
Extended polarization theorem to noncommutative variables
Provided computational formulas for determinants of space matrices
Abstract
This is a short review of some recent results obtained by the author. These results are related the problem of obtaining polynomial identities (computational formulas) for some matrix functions by means of the known polarization theorem, including the case of noncommutative variables and of determinant of space matrices.
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Taxonomy
TopicsRandom Matrices and Applications · Markov Chains and Monte Carlo Methods · Matrix Theory and Algorithms