Further results on generalized and hypergeneralized projectors

DOI10.1016/j.laa.2007.03.029zbMath1151.15022OpenAlexW1994800894MaRDI QIDQ935376

Jerzy K. Baksalary, Oskar Maria Baksalary, Götz Trenkler, Xiaoji Liu

Publication date: 6 August 2008

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

Full work available at URL: https://doi.org/10.1016/j.laa.2007.03.029

zbMATH Keywords

contractionmatrix partial orderingspartial isometrynormal matrixidempotent matrixEP matrixquadripotent matrixstar-dagger matrixweak-EP matrix

Mathematics Subject Classification ID

Theory of matrix inversion and generalized inverses (15A09) Positive matrices and their generalizations; cones of matrices (15B48) Hermitian, skew-Hermitian, and related matrices (15B57) Miscellaneous inequalities involving matrices (15A45)

Related Items (17)

The invertibility of the difference and the sum of commuting generalized and hypergeneralized projectors ⋮ A note on the differentiable structure of generalized idempotents ⋮ On matrices whose Moore–Penrose inverse is idempotent ⋮ On the equality between rank and trace of an idempotent matrix ⋮ Unnamed Item ⋮ On the matrix difference \({\mathbf I}-{\mathbf A}\) ⋮ The diamond partial order in rings ⋮ Matrices \(A\) such that \(A^{s+1}R\) = \(RA^\ast\) with \(R^k = I\) ⋮ On disjoint range matrices ⋮ Core inverse of matrices ⋮ On the projectors \(\mathbf F\mathbf F^\dagger\) and \(\mathbf F^\dagger\mathbf F\). ⋮ A note on the equality of rank and trace for an idempotent matrix ⋮ Partial isometries and pseudoinverses in semi-Hilbertian spaces ⋮ On angles and distances between subspaces ⋮ On a matrix decomposition of Hartwig and Spindelböck ⋮ The new revisitation of core EP inverse of matrices ⋮ Further results on the Moore–Penrose invertibility of projectors and its applications

Cites Work

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• Left-star and right-star partial orderings
• Partial orderings, preorderings, and the polar decomposition of matrices
• Generalized and hypergeneralized projectors
• Further properties of the star, left-star, right-star, and minus partial orderings.
• The spectral characterization of generalized projections
• Generalized inverses. Theory and applications.
• An alternative characterization of generalized projectors
• Further properties of generalized and hypergeneralized projectors
• A note on generalized and hypergeneralized projectors
• Matrices for whichA^∗andA^†commute
• Partial isometries, contractions and EP matrices
• The natural partial order on a regular semigroup
• Natural structures on semigroups with involution

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