NDLI: The Interplay of Ranks of Submatrices

Content Provider	Society for Industrial and Applied Mathematics (SIAM)
Author	Nguyen, Tri Strang, Gilbert
Copyright Year	2004
Abstract	A banded invertible matrix T has a remarkable inverse. All "upper" and "lower" submatrices of T-1 have low rank (depending on the bandwidth in T). The exact rank condition is known, and it allows fast multiplication by full matrices that arise in the boundary element method. We look for the "right" proof of this property of T-1 . Ultimately it reduces to a fact that deserves to be better known: Complementary submatrices of any T and T-1 have the same nullity. The last figure in the paper (when T is tridiagonal) shows that, on and above the diagonal of T-1 , all rows are proportional.
Starting Page	637
Ending Page	646
Page Count	10
File Format	PDF
ISSN	00361445
DOI	10.1137/S0036144503434381
e-ISSN	10957200
Journal	SIAM Review (SIREAD)
Issue Number	4
Volume Number	46
Language	English
Publisher	Society for Industrial and Applied Mathematics
Publisher Date	2006-08-04
Access Restriction	Subscribed
Subject Keyword	low rank submatrix fast multiplication Determinants, permanents, other special matrix functions Direct methods for linear systems and matrix inversion nullity theorem Matrix inversion, generalized inverses band matrix
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Theoretical Computer Science Computational Mathematics

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