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Marko Lindner, Gilbert Strang: The Main Diagonal of a Permutation Matrix

Marko Lindner, Gilbert Strang: The Main Diagonal of a Permutation Matrix

Author(s):
Marko Lindner
Gilbert Strang
Title:
The Main Diagonal of a Permutation Matrix
Electronic source:
application/pdf
Preprint series:
Technische Universität Chemnitz, Fakultät für Mathematik (Germany). Preprint 20, 2011
Mathematics Subject Classification:
15A23 []
47A53 []
47B36 []
Abstract:
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.
Keywords:
banded matrix, permutation, infinite matrix, main diagonal, factorization
Language:
English
Publication time:
12/2011