NDLI: Inertias of Block Band Matrix Completions

Content Provider	Society for Industrial and Applied Mathematics (SIAM)
Author	Dancis, Jerome Cohen, Nir
Copyright Year	1998
Abstract	This paper classifies the ranks and inertias of hermitian completion for the partially specified 3 x 3 block band hermitian matrix (also known as a "bordered matrix") P=\pmatrix{A&B&?\cr B^&C&D\cr ?&D^&E}. The full set of completion inertias is described in terms of seven linear inequalities involving inertias and ranks of specified submatrices. The minimal completion rank for P is computed.We study the completion inertias of partially specified hermitian block band matrices, using a block generalization of the Dym--Gohberg algorithm. At each inductive step, we use our classification of the possible inertias for hermitian completions of bordered matrices. We show that when all the maximal specified submatrices are invertible, any inertia consistent with Poincar's inequalities is obtainable. These results generalize the nonblock band results of Dancis [SIAM J. Matrix Anal. Appl., 14 (1993), pp. 813--829]. All our results remain valid for real symmetric completions.
Starting Page	583
Ending Page	612
Page Count	30
File Format	PDF
ISSN	08954798
DOI	10.1137/S0895479895296471
e-ISSN	10957162
Journal	SIAM Journal on Matrix Analysis and Applications (SJMAEL)
Issue Number	3
Volume Number	19
Language	English
Publisher	Society for Industrial and Applied Mathematics
Publisher Date	2006-07-31
Access Restriction	Subscribed
Subject Keyword	completion inertia rank minimal rank hermitian matrices
Content Type	Text
Resource Type	Article
Subject	Analysis

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