On Moore-Penrose Inverse of Block Matrices and Full-rank Factorization
Gradimir V. Milovanović, Predrag Stanimirović (1997)
Publications de l'Institut Mathématique
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Gradimir V. Milovanović, Predrag Stanimirović (1997)
Publications de l'Institut Mathématique
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Stanimirović, P. (1996)
Matematichki Vesnik
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Yong Ge Tian, George P. H. Styan (2002)
Commentationes Mathematicae Universitatis Carolinae
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It is shown that where is idempotent, has full row rank and . Some applications of the rank formula to generalized inverses of matrices are also presented.
Yunkun Chen, Xinghua Shi, Yi Min Wei (2016)
Czechoslovak Mathematical Journal
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We extend Rump's verified method (S. Oishi, K. Tanabe, T. Ogita, S. M. Rump (2007)) for computing the inverse of extremely ill-conditioned square matrices to computing the Moore-Penrose inverse of extremely ill-conditioned rectangular matrices with full column (row) rank. We establish the convergence of our numerical verified method for computing the Moore-Penrose inverse. We also discuss the rank-deficient case and test some ill-conditioned examples. We provide our Matlab codes for...
Bapat, R.B., Zheng, Bing (2003)
ELA. The Electronic Journal of Linear Algebra [electronic only]
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Jeremy Lovejoy, Robert Osburn (2010)
Acta Arithmetica
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Catral, Minerva, Olesky, Dale D., van den Driessche, Pauline (2009)
ELA. The Electronic Journal of Linear Algebra [electronic only]
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Bu, Changjiang, Zhao, Jiemei, Zhang, Kuize (2009)
ELA. The Electronic Journal of Linear Algebra [electronic only]
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Dragan S. Đorđević, Predrag Stanimirović (1999)
Matematički Vesnik
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Yongge Tian (2010)
Open Mathematics
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A complex square matrix A is called an orthogonal projector if A 2 = A = A*, where A* denotes the conjugate transpose of A. In this paper, we give a comprehensive investigation to matrix expressions consisting of orthogonal projectors and their properties through ranks of matrices. We first collect some well-known rank formulas for orthogonal projectors and their operations, and then establish various new rank formulas for matrix expressions composed by orthogonal projectors. As applications,...
Bernard Aupetit, H. Mouton (1996)
Studia Mathematica
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We show that the trace and the determinant on a semisimple Banach algebra can be defined in a purely spectral and analytic way and then we obtain many consequences from these new definitions.
R. M. Brits, L. Lindeboom, H. Raubenheimer (2006)
Studia Mathematica
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Let A be an arbitrary, unital and semisimple Banach algebra with nonzero socle. We investigate the relationship between the spectral rank (defined by B. Aupetit and H. Mouton) and the Drazin index for elements belonging to the socle of A. In particular, we show that the results for the finite-dimensional case can be extended to the (infinite-dimensional) socle of A.