Completely Positive Matrices

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  • Completely Positive Matrices Book Detail

  • Author : Abraham Berman
  • Release Date : 2003
  • Publisher : World Scientific
  • Genre : Mathematics
  • Pages : 222
  • ISBN 13 : 9789812795212
  • File Size : 77,77 MB

Completely Positive Matrices by Abraham Berman PDF Summary

Book Description: A real matrix is positive semidefinite if it can be decomposed as A = BBOC . 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 = BBOC 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. Contents: Preliminaries: Matrix Theoretic Background; Positive Semidefinite Matrices; Nonnegative Matrices and M -Matrices; Schur Complements; Graphs; Convex Cones; The PSD Completion Problem; Complete Positivity: Definition and Basic Properties; Cones of Completely Positive Matrices; Small Matrices; Complete Positivity and the Comparison Matrix; Completely Positive Graphs; Completely Positive Matrices Whose Graphs are Not Completely Positive; Square Factorizations; Functions of Completely Positive Matrices; The CP Completion Problem; CP Rank: Definition and Basic Results; Completely Positive Matrices of a Given Rank; Completely Positive Matrices of a Given Order; When is the CP-Rank Equal to the Rank?. Readership: Upper level undergraduates, graduate students, academics and researchers interested in matrix theory."

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Completely Positive Matrices

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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

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A real matrix is positive semidefinite if it can be decomposed as A = BBOC . In some applications the matrix B has to be elementwise nonnegative. If such a matr

Completely Positive Matrices

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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 e

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This book represents the first synthesis of the considerable body of new research into positive definite matrices. These matrices play the same role in noncommu