On the equality between rank and trace of an idempotent matrix

DOI10.1016/j.amc.2010.10.022zbMath1206.15006OpenAlexW1988065212MaRDI QIDQ618106

Dennis S. Bernstein, Götz Trenkler, Oskar Maria Baksalary

Publication date: 14 January 2011

Published in: Applied Mathematics and Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.amc.2010.10.022

zbMATH Keywords

tracerankMoore-Penrose inverseoblique projectoridempotent matrixorthogonal projectorpartitioned matrix

Mathematics Subject Classification ID

Theory of matrix inversion and generalized inverses (15A09) Determinants, permanents, traces, other special matrix functions (15A15) Vector spaces, linear dependence, rank, lineability (15A03)

Related Items (8)

Unique builders for classes of matrices ⋮ Unnamed Item ⋮ Fractionalization of a discrete Hankel transform based on an involutory symmetric kernel matrix ⋮ Systems of MDS codes from units and idempotents ⋮ A brief derivation of necessary and sufficient conditions for a family of matrix quadratic forms to have mutually independent non-central Wishart distributions ⋮ A note on the equality of rank and trace for an idempotent matrix ⋮ Representations of group rings and groups ⋮ Idempotents in triangular matrix rings

Cites Work

• Further results on generalized and hypergeneralized projectors
• On a matrix decomposition of Hartwig and Spindelböck
• A note on idempotent matrices
• Powers of matrices and idempotency
• On the product of orthogonal projectors
• Rank formulae from the perspective of orthogonal projectors
• Matrices for whichA^∗andA^†commute
• Some Applications of the Pseudoinverse of a Matrix
• Matrix theory. Basic results and techniques
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