Schur complements obey Lambek's categorial grammar: Another view of Gaussian elimination and LU decomposition

DOI10.1016/S0024-3795(97)10033-7zbMath0933.65026MaRDI QIDQ1307278

V. Pereyra

Publication date: 19 December 1999

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

zbMATH Keywords

Gaussian eliminationLambek calculusSchur complementsLU-decompositionquotientscategorial grammar

Mathematics Subject Classification ID

Theory of languages and software systems (knowledge-based systems, expert systems, etc.) for artificial intelligence (68T35) Natural language processing (68T50) Direct numerical methods for linear systems and matrix inversion (65F05)

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Cites Work

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• Determinantal identities: Gauss, Schur, Cauchy, Sylvester, Kronecker, Jacobi, Binet, Laplace, Muir, and Cayley
• Manifestations of the Schur complement
• Multimodal linguistic inference
• Determination of the inertia of a partitioned Hermitian matrix
• Reduction of a matrix using properties of the Schur complement
• A new proof of Haynsworth's quotient formula for Schur complements
• The Mathematics of Sentence Structure
• An Identity for the Schur Complement of a Matrix
• Applications of an Inequality for the Schur Complement
• A Generalization of the Schur Complement by Means of the Moore–Penrose Inverse

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