Solutions of the matrix equation p(X)=A, with polynomial function p(λ) over field extensions of Q

Autor: G.J. Groenewald, D.B. Janse van Rensburg, A.C.M. Ran, F. Theron, M. van Straaten
Přispěvatelé: Mathematics
Jazyk: angličtina
Rok vydání: 2023
Předmět:
Zdroj: Groenewald, G J, Janse van Rensburg, D B, Ran, A C M, Theron, F & van Straaten, M 2023, ' Solutions of the matrix equation p(X)=A, with polynomial function p(λ) over field extensions of Q ', Linear Algebra and its Applications, vol. 665, pp. 107-138 . https://doi.org/10.1016/j.laa.2023.01.028
Linear Algebra and its Applications, 665, 107-138. Elsevier Inc.
ISSN: 0024-3795
DOI: 10.1016/j.laa.2023.01.028
Popis: Let H be a field with Q⊆H⊆C, and let p(λ) be a polynomial in H[λ], and let A∈Hn×n be nonderogatory. In this paper we consider the problem of finding a solution X∈Hn×n to p(X)=A. A necessary condition for this to be possible is already known from a paper by M.P. Drazin: Exact rational solutions of the matrix equation A=p(X) by linearization. Under an additional condition we provide an explicit construction of such solutions. The similarities and differences with the derogatory case will be discussed as well. One of the tools needed in the paper is a new canonical form, which may be of independent interest. It combines elements of the rational canonical form with elements of the Jordan canonical form.
Databáze: OpenAIRE
Externí odkaz: