The main diagonal of a permutation matrix
Name
Strang_The main diagonal.pdf
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242.17 KB
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Author(s)
Lindner, Marko
Strang, Gilbert
Date Issued
May 2012
Journal
Linear Algebra and its Applications
Publisher
Elsevier
Citation
Lindner, Marko, and Gilbert Strang. “The Main Diagonal of a Permutation Matrix.” Linear Algebra and Its Applications 439, no. 3 (August 2013): 524–537.
Version
Author's final manuscript
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.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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Creative Commons Attribution-Noncommercial-NoDerivatives
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DOI of Published Version
https://doi.org/10.1016/j.laa.2012.02.034
