Restricted quadratic forms, inertia theorems, and the Schur complement
type: Item
instance of: scholarly article
title: Restricted quadratic forms, inertia theorems, and the Schur complement
zbMATH Open document ID: 0653.15020
DOI: 10.1016/0024-3795(88)90177-2
published in: Linear Algebra and its Applications
publication date: 1988-01-01T00:00:00Z
full work available at URL: http://hdl.handle.net/1903/4627
review text: Let A be a real \(m\times m\) symmetric matrix, then x \(tAx=Q(x)\) is a quadratic form on a real m-dimensional vector space. The inertia of A is the triple (p,q,r), where p, q, and r are the numbers of positive, negative, and zero eigenvectors of A, respectively. For any subspace S of R m the restriction of Q to S is again a quadratic form. The author proves a number of theorems on the inertia of this restriction, inertia formulas involving the Moore-Penrose inverse of A, inertia formulas for partitioned matrices and for the generalized Schur complement of A.
Mathematics Subject Classification ID: 15A63
Mathematics Subject Classification ID: 15A18
Mathematics Subject Classification ID: 15A42
zbMATH DE Number: 4065188
zbMATH Keywords: symmetric matrix
zbMATH Keywords: quadratic form
zbMATH Keywords: inertia
zbMATH Keywords: Moore-Penrose inverse
zbMATH Keywords: partitioned matrices
zbMATH Keywords: Schur complement
author: J. H. Maddocks
reviewed by: Erich W. Ellers
MaRDI profile type: Publication
OpenAlex ID: W2132929299
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description: scientific article; zbMATH DE number 4065188