A NEW APPROACH TO SOLVING MATRIX PROBLEMS ON A SET OF NONCOMMUTATIVE MATRICES
DOI:
https://doi.org/10.15407/dopovidi2025.06.015Keywords:
recurrence relation, minimal order differential equation, Laguerre—Cayley, Laguerre, Hermite matrix polynomials, fundamental Lagrange matrix polynomialsAbstract
A unique statement has been formulated — Makarov’s thesis, which allows one to construct matrix polynomials on a set of noncommutative matrices and study the properties of these polynomials based on their scalar analogues. The article is devoted to demonstrating the power of the thesis and its unique application possibilities in mathematics, mechanics, and other sciences where matrix mathematical models arise, using non-trivial examples.
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