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

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• 作者：Parker ; D. Stott
• 关键词：Schur complements ; Quotients ; Categorial grammar ; Categorical grammar ; Lambek calculus ; Gaussian elimination ; LU decomposition
• 刊名：Linear Algebra and its Applications
• 出版年：1998
• 期刊代码：38_00243795
• 类别：mt
• 出版时间：July 15, 1998
• 卷：278
• 期：1-3
• 页码：63-84
• 文件大小：710 K

摘要

For three decades Schur complements have seen increasing applications in linear algebra, often as abstractions of Gaussian elimination. It is known that they obey certain nontrivial identities, such as Crabtree and Haynsworth's quotient property. We began this work asking if there were a theory for deciding their properties in general.