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