Completely Positive Matrices

ISBN-13: 9789812383686 / Angielski / Twarda / 2003 / 216 str.

Abraham Berman; Naomi Shaked-Monderer;Shaked-Monderer-Naomi

Opis

A real matrix is positive semidefinite if it can be decomposed as A=BBT. In some applications the matrix B has to be elementwise nonnegative. If such a matrix exists, A is called completely positive. The smallest number of columns of a nonnegative matrix B such that A=BBT is known as the cp-rank of A.

This invaluable book focuses on necessary conditions and sufficient conditions for complete positivity, as well as bounds for the cp-rank. The methods are combinatorial, geometric and algebraic. The required background on nonnegative matrices, cones, graphs and Schur complements is outlined.