Completely Positive Matrices
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.