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The Main Diagonal of a Permutation Matrix

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arxiv 1112.0582 v2 pith:2UFK5JL5 submitted 2011-12-02 math.NA cs.NA

Marko Lindner , Gilbert Strang This is my paper · ORCID
classification math.NAcs.NA
keywords diagonalmainmatrixpermutationdeterminedinfinitematricesrows
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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.

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