03177nam 22006014a 450 991045429550332120200520144314.01-281-93563-89786611935634981-279-521-9(CKB)1000000000537829(DLC)2004269154(StDuBDS)AH24685168(SSID)ssj0000127202(PQKBManifestationID)11936900(PQKBTitleCode)TC0000127202(PQKBWorkID)10051708(PQKB)10571981(MiAaPQ)EBC1681529(WSP)00005273(PPN)18135621X(Au-PeEL)EBL1681529(CaPaEBR)ebr10255679(CaONFJC)MIL193563(OCoLC)815752525(EXLCZ)99100000000053782920040205d2003 uy 0engur|||||||||||txtccrCompletely positive matrices[electronic resource] /Abraham Berman, Naomi Shaked-Monderer[River Edge] New Jersey World Scienficc20031 online resource (ix, 206 p. ) illBibliographic Level Mode of Issuance: Monograph981-238-368-9 Includes bibliographical references (p. 193-197) and index.ch. 1. Preliminaries. 1.1. Matrix theoretic background. 1.2. Positive semidefinite matrices. 1.3. Nonnegative matrices and M-matrices. 1.4. Schur complements. 1.5. Graphs. 1.6. Convex cones. 1.7. The PSD completion problem -- ch. 2. Complete positivity. 2.1. Definition and basic properties. 2.2. Cones of completely positive matrices. 2.3. Small matrices. 2.4. Complete positivity and the comparison matrix. 2.5. Completely positive graphs. 2.6. Completely positive matrices whose graphs are not completely positive. 2.7. Square factorizations. 2.8. Functions of completely positive matrices. 2.9. The CP completion problem -- ch. 3. CP rank. 3.1. Definition and basic results. 3.2. Completely positive matrices of a given rank. 3.3. Completely positive matrices of a given order. 3.4. When is the cp-rank equal to the rank?A real matrix is positive semidefinite if it can be decomposed as A=BB[symbol]. 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[symbol] 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.MatricesElectronic books.Matrices.512.9/434Berman Abraham42972Shaked-Monderer Naomi906214MiAaPQMiAaPQMiAaPQBOOK9910454295503321Completely positive matrices2026800UNINA