English

Principal pivot transforms: properties and applications

Rings and Algebras 2007-05-23 v1

Abstract

The principal pivot transform (PPT) of a matrix A partitioned relative to an invertible leading principal submatrix is a matrix B such that A [x_1^T x_2^T]^T = [y_1^T y_2^T]^T if and only if B [y_1^T x_2^T]^T = [x_1^T y_2^T]^T, where all vectors are partitioned conformally to A. The purpose of this paper is to survey the properties and manifestations of PPTs relative to arbitrary principal submatrices, make some new observations, present and possibly motivate further applications of PPTs in matrix theory. We pay special attention to PPTs of matrices whose principal minors are positive.

Keywords

Cite

@article{arxiv.math/9807132,
  title  = {Principal pivot transforms: properties and applications},
  author = {Michael Tsatsomeros},
  journal= {arXiv preprint arXiv:math/9807132},
  year   = {2007}
}

Comments

12 pages, LaTex2e file