Principal pivot transforms: properties and applications
Michael Tsatsomeros
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 [x1T x2T]T = [y1T y2T]T if and only if B [y1T x2T]T = [x1T y2T]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.
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