Organized into 10 chapters, this book begins with an overview of the properties of nonnegative matrices. This text then examines the inverse-positive matrices. Other chapters consider the basic approaches to the study of nonnegative matrices, namely, geometrical and combinatorial. This book discusses as well some useful ideas from the algebraic theory of semigroups and considers a canonical form for nonnegative idempotent matrices and special types of idempotent matrices. The final chapter deals with the linear complementary problem (LCP).
This book is a valuable resource for mathematical economists, mathematical programmers, statisticians, mathematicians, and computer scientists.
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 BackgroundPositive Semidefinite MatricesNonnegative Matrices and M-MatricesSchur ComplementsGraphsConvex ConesThe PSD Completion ProblemComplete Positivity:Definition and Basic PropertiesCones of Completely Positive MatricesSmall MatricesComplete Positivity and the Comparison MatrixCompletely Positive GraphsCompletely Positive Matrices Whose Graphs are Not Completely PositiveSquare FactorizationsFunctions of Completely Positive MatricesThe CP Completion ProblemCP Rank:Definition and Basic ResultsCompletely Positive Matrices of a Given RankCompletely Positive Matrices of a Given OrderWhen is the CP-Rank Equal to the Rank?
Readership: Upper level undergraduates, graduate students, academics and researchers interested in matrix theory.
Keywords:Reviews:“Overall, this appears to be a highly delightful book to read, study, and teach from.”Zentralblatt MATH
“The topics are of interest mainly from an applied mathematician's point of view, but the techniques and the difficulties make them appealing for the pure mathematician as well.”Mathematical Reviews