The main diagonal of a permutation matrix

Publikationstyp
Journal Article
Date Issued
2012-05-03
Sprache
English
Author(s)
Lindner, Marko  orcid-logo
Strang, Gilbert  
Institut
Mathematik E-10  
TORE-URI
http://hdl.handle.net/11420/3166
Journal
Linear algebra and its applications  
Volume
439
Issue
3
Start Page
524
End Page
537
Citation
Linear Algebra and Its Applications 3 (439): 524-537 (2013)
Publisher DOI
10.1016/j.laa.2012.02.034
Scopus ID
2-s2.0-84878302360
Publisher
American Elsevier Publ.
By counting 1's in the "right half" of 2w consecutive rows, we locate the main diagonal of any doubly infinite permutation matrix with bandwidth w. Then the matrix can be correctly centered and factored into block-diagonal permutation matrices. Part II of the paper discusses the same questions for the much larger class of band-dominated matrices. The main diagonal is determined by the Fredholm index of a singly infinite submatrix. Thus the main diagonal is determined "at infinity" in general, but from only 2w rows for banded permutations.
Subjects
banded matrix
permutation
ifinite matrix
main diagonal
factorization
DDC Class
510: Mathematik
More Funding Information
Marie-Curie Grant of the European Union