Completely Positive Matrices

ISBN: 9789812383686

出版社: World Scientific Pub Co Inc

页数: 206

定价: $ 97.18

装帧: HRD

内容简介

A real matrix is positive semidefinite if it can be decomposed as A=BB'. 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=BB' 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. Upper level undergraduates, graduate students, academics and researchers interested in matrix theory.