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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Displaying similar documents to “Algorithms 80-81. Calculation of projections”
On Moore-Penrose Inverse of Block Matrices and Full-rank Factorization
General determinantal representation of pseudoinverses.
Stanimirović, P. (1996)
Matematichki Vesnik
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A new rank formula for idempotent matrices with applications
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.
Convergence of Rump's method for computing the Moore-Penrose inverse
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...
Generalized inverses of bordered matrices.
Bapat, R.B., Zheng, Bing (2003)
ELA. The Electronic Journal of Linear Algebra [electronic only]
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M₂-rank differences for overpartitions
Jeremy Lovejoy, Robert Osburn (2010)
Acta Arithmetica
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Block representations of the Drazin inverse of a bipartite matrix.
Catral, Minerva, Olesky, Dale D., van den Driessche, Pauline (2009)
ELA. The Electronic Journal of Linear Algebra [electronic only]
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Some results on the group inverse for block matrices over skew fields.
Bu, Changjiang, Zhao, Jiemei, Zhang, Kuize (2009)
ELA. The Electronic Journal of Linear Algebra [electronic only]
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General Representation of Pseudoinverses
Dragan S. Đorđević, Predrag Stanimirović (1999)
Matematički Vesnik
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Equalities for orthogonal projectors and their operations
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,...