Quantum Physics Division
Faculty of PhysicsAdam Mickiewicz University
Publications

Polynomials satsfiedd by two linked matrices

O. M. Baksalary1 , J. Hauke2 , Ch. R. Johnson3

1 Institute of Physics, Adam Mickiewicz University, ul. Umultowska 85, PL 61-614 Poznań, Poland
2 Institute of Socio-Economic Geography and Spatial Management, Adam Mickiewicz University, ul. Dzięgielowa 27, PL 61-680 Poznań, Poland
3 Department of Mathematics, The College of William and Mary, Williamsburg, VA 23187-8795, USA

Linear Algebra and Its Applications, 429, 2335 (2008)
DOI: 10.1016/j.laa.2008.05.003

Abstract:

Polynomials in two variables, evaluated at A and "A" source with A being a square complex matrix and View the "A" source 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 "A" source. The results given unify a number of prior, isolated results.

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