The Main Diagonal of a Permutation Matrix
Numerical Analysis
2011-12-16 v2
Abstract
By counting 1's in the "right half" of consecutive rows, we locate the main diagonal of any doubly infinite permutation matrix with bandwidth . 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 rows for banded permutations.
Cite
@article{arxiv.1112.0582,
title = {The Main Diagonal of a Permutation Matrix},
author = {Marko Lindner and Gilbert Strang},
journal= {arXiv preprint arXiv:1112.0582},
year = {2011}
}