Displaying similar documents to “On the relation between Moore's and Penrose's conditions.”

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...

Positive splittings of matrices and their nonnegative Moore-Penrose inverses

Tamminana Kurmayya, Koratti C. Sivakumar (2008)

Discussiones Mathematicae - General Algebra and Applications

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In this short note we study necessary and sufficient conditions for the nonnegativity of the Moore-Penrose inverse of a real matrix in terms of certain spectral property shared by all positive splittings of the given matrix.

On the generalized Drazin inverse and generalized resolvent

Dragan S. Djordjević, Stanimirović, Predrag S. (2001)

Czechoslovak Mathematical Journal

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We investigate the generalized Drazin inverse and the generalized resolvent in Banach algebras. The Laurent expansion of the generalized resolvent in Banach algebras is introduced. The Drazin index of a Banach algebra element is characterized in terms of the existence of a particularly chosen limit process. As an application, the computing of the Moore-Penrose inverse in C * -algebras is considered. We investigate the generalized Drazin inverse as an outer inverse with prescribed range...

Some equalities for generalized inverses of matrix sums and block circulant matrices

Yong Ge Tian (2001)

Archivum Mathematicum

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Let A 1 , A 2 , ⋯ , A n be complex matrices of the same size. We show in this note that the Moore-Penrose inverse, the Drazin inverse and the weighted Moore-Penrose inverse of the sum ∑ t = 1 n A t can all be determined by the block circulant matrix generated by A 1 , A 2 , ⋯ , A n . In addition, some equalities are also presented for the Moore-Penrose inverse and the Drazin inverse of a quaternionic matrix.