Revisitation of the product of two orthogonal projectors

DOI10.1016/j.laa.2009.01.020zbMath1167.15018OpenAlexW2113867048MaRDI QIDQ1017642

Oskar Maria Baksalary, Götz Trenkler

Publication date: 12 May 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.2009.01.020

zbMATH Keywords

tracespectral propertiesrankrangegeneralized inversesMoore-Penrose inversegroup inversenull spaceHermitian idempotent matrixspectral normpartitioned matrixfunctions of orthogonal projectors

Mathematics Subject Classification ID

Theory of matrix inversion and generalized inverses (15A09) Determinants, permanents, traces, other special matrix functions (15A15) Matrix equations and identities (15A24) Eigenvalues, singular values, and eigenvectors (15A18) Norms of matrices, numerical range, applications of functional analysis to matrix theory (15A60) Hermitian, skew-Hermitian, and related matrices (15B57) Vector spaces, linear dependence, rank, lineability (15A03)

Related Items (16)

On matrices whose Moore–Penrose inverse is idempotent ⋮ Products of orthogonal projections and polar decompositions ⋮ On the invertibility and range closedness of the linear combinations of a pair of projections ⋮ Representation of projectors involving Minkowski inverse in Minkowski space ⋮ On disjoint range operators in a Hilbert space ⋮ Revisitation of the core inverse ⋮ Revisiting the core EP inverse and its extension to rectangular matrices ⋮ On disjoint range matrices ⋮ On the projectors \(\mathbf F\mathbf F^\dagger\) and \(\mathbf F^\dagger\mathbf F\). ⋮ The range and kernel relations of a pair of projections ⋮ On relationships between two linear subspaces and two orthogonal projectors ⋮ Unnamed Item ⋮ The new revisitation of core EP inverse of matrices ⋮ Operators with compatible ranges ⋮ Relating moments of self-adjoint polynomials in two orthogonal projections ⋮ Further results on the Moore–Penrose invertibility of projectors and its applications

Cites Work

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• ON THE LATENT VECTORS AND CHARACTERISTIC VALUES OF PRODUCTS OF PAIRS OF SYMMETRIC IDEMPOTENTS
• Eigenvalues of the difference and product of projections
• Solutions of the Matrix Equation $XAX = X$, and Relations between Oblique and Orthogonal Projectors
• On Generalized Inverses of Matrices
• Rank equalities for idempotent and involutory matrices

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