Completely Positive Matrices By Abraham Berman, Naomi Shaked-Monderer

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Completely Positive Matrices
By Abraham Berman, Naomi Shaked-Monderer



  • Publisher: World Scientific Publishing Company
  • Number Of Pages: 216
  • Publication Date: 2003-04
  • ISBN-10 / ASIN: 9812383689
  • ISBN-13 / EAN: 9789812383686
  • Binding: Hardcover


Product Description:
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 work 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.​



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