Polynomials satisfied by two linked matrices |
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Authors: | Oskar Maria Baksalary Jan Hauke |
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Institution: | a Faculty of Physics, Adam Mickiewicz University, ul. Umultowska 85, PL 61-614 Poznań, Poland b Institute of Socio-Economic Geography and Spatial Management, Adam Mickiewicz University, ul. Dzi?gielowa 27, PL 61-680 Poznań, Poland c Department of Mathematics, The College of William and Mary, Williamsburg, VA 23187-8795, USA |
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Abstract: | Polynomials in two variables, evaluated at A and with A being a square complex matrix and being its transform belonging to the set {A=, A†, A∗}, in which A=, A†, and A∗ denote, respectively, any reflexive generalized inverse, the Moore-Penrose inverse, and the conjugate transpose of A, are considered. An essential role, in characterizing when such polynomials are satisfied by two matrices linked as above, is played by the condition that the column space of A is the column space of . The results given unify a number of prior, isolated results. |
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Keywords: | 15A09 15A24 15A27 |
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