Particular formulae for the Moore-Penrose inverse of a columnwise partitioned matrix |
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Authors: | Jerzy K Baksalary Oskar Maria Baksalary |
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Institution: | a Faculty of Mathematics, Informatics and Econometrics, Zielona Góra University, ul. Podgórna 50, PL 65-246 Zielona Góra, Poland b Institute of Physics, Adam Mickiewicz University, ul. Umultowska 85, PL 61-614 Poznań, Poland |
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Abstract: | An essential part of Cegielski’s Obtuse cones and Gram matrices with non-negative inverse, Linear Algebra Appl. 335 (2001) 167-181] considerations of some properties of Gram matrices with nonnegative inverses, which are pointed out to be crucial in constructing obtuse cones, consists in developing some particular formulae for the Moore-Penrose inverse of a columnwise partitioned matrix A = (A1 : A2) under the assumption that it is of full column rank. In the present paper, these results are generalized and extended. The generalization consists in weakening the assumption mentioned above to the requirement that the ranges of A1 and A2 are disjoint, while the extension consists in introducing the conditions referring to the class of all generalized inverses of A. |
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Keywords: | 15A09 15A48 |
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