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.
| Identifer | oai:union.ndltd.org:DRESDEN/oai:qucosa.de:bsz:ch1-qucosa-80273 |
| Date | 11 July 2012 |
| Creators | Lindner, Marko, Strang, Gilbert |
| Contributors | TU Chemnitz, Fakultät für Mathematik, MIT (Massachusetts Institute of Technology), Department of Mathematics |
| Publisher | Universitätsbibliothek Chemnitz |
| Source Sets | Hochschulschriftenserver (HSSS) der SLUB Dresden |
| Language | English |
| Detected Language | English |
| Type | doc-type:preprint |
| Format | application/pdf, text/plain, application/zip |
| Relation | dcterms:isPartOf:Preprintreihe der Fakultät für Mathematik der TU Chemnitz, Preprint 2011-20 |
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