Principal pivot transforms: properties and applications Original Research Article

The principal pivot transform (PPT) is a transformation of the matrix of a linear system tantamount to exchanging unknowns with the corresponding entries of the right-hand side of the system. The notion of the PPT is encountered in mathematical programming, statistics and numerical analysis among other areas. The purpose of this paper is to draw attention to the main properties and uses of PPTs, make some new observations and motivate further applications of PPTs in matrix theory. Special consideration is given to PPTs of matrices whose principal minors are positive.