A new proof of Haynsworth's quotient formula for Schur complements

DOI10.1016/0024-3795(71)90010-3zbMath0224.15003OpenAlexW2038502386WikidataQ105570369 ScholiaQ105570369MaRDI QIDQ2548283

Alexander Ostrowski

Publication date: 1971

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

Full work available at URL: https://doi.org/10.1016/0024-3795(71)90010-3

Mathematics Subject Classification ID

Linear equations (linear algebraic aspects) (15A06)

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Pseudo-Schur complements and their properties, A Matrix Identity on the Schur Complement, A Schur complement approach to a general extrapolation algorithm, Schur complements and statistics, Compatibility and Schur complements of operators on Hilbert \(C^*\)-module, Schur complements and LDU decomposition in an additive category, Some generalized inverses of partition matrix and quotient identity of generalized Schur complement, Totally positive matrices, On manifestations of the Schur complement, Representations of generalized inverses and Drazin inverse of partitioned matrix with Banachiewicz-Schur forms, Generalized Schur complements, On Schur's complement, Determinantal identities: Gauss, Schur, Cauchy, Sylvester, Kronecker, Jacobi, Binet, Laplace, Muir, and Cayley, Manifestations of the Schur complement, Schur complements obey Lambek's categorial grammar: Another view of Gaussian elimination and LU decomposition

Cites Work

• Reduction of a matrix using properties of the Schur complement
• An Identity for the Schur Complement of a Matrix
• Applications of an Inequality for the Schur Complement