Matrices A such that AA − AA are nonsingular |
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| Authors: | Julio Benítez Vladimir Rako?evi? |
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| Institution: | a Departamento de Matemática Aplicada, Instituto de Matemática Multidisciplinar, Universidad Politécnica de Valencia, Camino de Vera s/n, 46022 Valencia, Spain
b Department of Mathematics, Faculty of Science and Mathematics, University of Niš Višegradska, 33, 18000 Niš, Serbia |
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| Abstract: | In this paper we study the class of square matrices A such that AA† − A†A is nonsingular, where A† stands for the Moore-Penrose inverse of A. Among several characterizations we prove that for a matrix A of order n, the difference AA† − A†A is nonsingular if and only if R(A)⊕R(A∗)=Cn,1, where R(·) denotes the range space. Also we study matrices A such that R(A)⊥=R(A∗). |
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| Keywords: | Co-EP matrices Moore-Penrose inverse Idempotent Orthogonal projectors |
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