The Drazin inverses of sum and difference of idempotents

DOI10.1016/j.laa.2008.10.017zbMath1161.47001OpenAlexW1973972381MaRDI QIDQ999806

Chun-Yuan Deng

Publication date: 10 February 2009

Published in: Linear Algebra and its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.laa.2008.10.017

zbMATH Keywords

idempotentDrazin inverse

Mathematics Subject Classification ID

Theory of matrix inversion and generalized inverses (15A09) Hilbert and pre-Hilbert spaces: geometry and topology (including spaces with semidefinite inner product) (46C05) General (adjoints, conjugates, products, inverses, domains, ranges, etc.) (47A05) Hilbert subspaces (= operator ranges); complementation (Aronszajn, de Branges, etc.) (46C07)

Related Items (31)

Unnamed Item ⋮ Some results on the Drazin invertibility and idempotents ⋮ Characterizations and representations of the Drazin inverse involving idempotents ⋮ A gentle guide to the basics of two projections theory ⋮ On properties of generalized quadratic operators ⋮ Classification of the finite-dimensional algebras generated by two tightly coupled idempotents. ⋮ Drazin inversion in the von Neumann algebra generated by two orthogonal projections ⋮ The Drazin invertibility of the difference and the sum of two idempotent operators ⋮ The Drazin inverse of the sum of two matrices and its applications ⋮ On the Drazin inverse of the sum of two matrices ⋮ Characterizations and representations of the group inverse involving idempotents ⋮ Drazin and group invertibility in algebras spanned by two idempotents ⋮ Relationships between different sets involving group and Drazin projectors and nonnegativity ⋮ The Drazin inverse of the linear combinations of two idempotents in the Banach algebra ⋮ On the idempotent solutions of a kind of operator equations ⋮ On the Drazin inverse of the linear combinations of two idempotents in a complex Banach algebra ⋮ Generalized Drazin invertibility of combinations of idempotents ⋮ Some additive results on Drazin inverse ⋮ Drazin Invertibility in a Certain Finite-Dimensional Algebra Generated by Two Idempotents ⋮ On the invertibility of the operatorA-XB ⋮ Group inversion in certain finite-dimensional algebras generated by two idempotents ⋮ On certain finite-dimensional algebras generated by two idempotents ⋮ The Drazin inverses of infinite triangular matrices and their linear preservers ⋮ The representations of the Drazin inverse of differences of two matrices ⋮ Nonsingularity and group invertibility of linear combinations of twok-potent matrices ⋮ A note on computational formulas for the Drazin inverse of certain block matrices ⋮ The group inverse and core inverse of sums of two elements in a ring ⋮ Additive results for the group inverse in an algebra with applications to block operators ⋮ The Drazin and generalized Drazin invertibility of linear combinations of idempotents ⋮ Reverse order law for the Drazin inverse in Banach spaces ⋮ The core inverses of linear combinations of two core invertible matrices

Cites Work

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• The Drazin inverse of updating of a square matrix with application to perturbation formula
• Additive perturbation results for the Drazin inverse
• Representations of the Drazin inverse for a class of block matrices
• The Drazin inverses of products and differences of orthogonal projections
• Additive results for the generalized Drazin inverse
• Pseudo-Inverses in Associative Rings and Semigroups
• On the Generalized Drazin Inverse and Generalized Resolvent
• APPLICATIONS OF THE DRAZIN INVERSE TO THE HILL CRYPTOGRAPHIC SYSTEM. PART III.
• The Condition of a Finite Markov Chain and Perturbation Bounds for the Limiting Probabilities
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• Some additive results on Drazin inverse

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