English

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.

Keywords

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

R2 v1 2026-06-22T00:52:17.336Z