Mathematics – Rings and Algebras
Scientific paper
1998-07-23
Linear Algebra and Its Applications, 300:151-165, 2000
Mathematics
Rings and Algebras
12 pages, LaTex2e file
Scientific paper
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.
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