The Nullity Theorem for Principal Pivot Transform
Combinatorics
2014-03-26 v2
Abstract
We generalize the nullity theorem of Gustafson [Linear Algebra Appl. (1984)] from matrix inversion to principal pivot transform. Several special cases of the obtained result are known in the literature, such as a result concerning local complementation on graphs. As an application, we show that a particular matrix polynomial, the so-called nullity polynomial, is invariant under principal pivot transform.
Cite
@article{arxiv.1307.4272,
title = {The Nullity Theorem for Principal Pivot Transform},
author = {Robert Brijder},
journal= {arXiv preprint arXiv:1307.4272},
year = {2014}
}
Comments
5 pages, no figures