LEADER 03177nam  22006014a 450 
001 9910454295503321
005 20200520144314.0
010   $a1-281-93563-8
010   $a9786611935634
010   $a981-279-521-9
035   $a(CKB)1000000000537829
035   $a(DLC)2004269154
035   $a(StDuBDS)AH24685168
035   $a(SSID)ssj0000127202
035   $a(PQKBManifestationID)11936900
035   $a(PQKBTitleCode)TC0000127202
035   $a(PQKBWorkID)10051708
035   $a(PQKB)10571981
035   $a(MiAaPQ)EBC1681529
035   $a(WSP)00005273
035   $a(PPN)18135621X
035   $a(Au-PeEL)EBL1681529
035   $a(CaPaEBR)ebr10255679
035   $a(CaONFJC)MIL193563
035   $a(OCoLC)815752525
035   $a(EXLCZ)991000000000537829
100   $a20040205d2003      uy             0
101 0 $aeng
135   $aur|||||||||||
181   $ctxt
182   $cc
183   $acr
200 10$aCompletely positive matrices$b[electronic resource] /$fAbraham Berman, Naomi Shaked-Monderer
210   $a[River Edge] New Jersey $cWorld Scienfic$dc2003
215   $a1 online resource (ix, 206 p.  ) $cill
300   $aBibliographic Level Mode of Issuance: Monograph
311   $a981-238-368-9 
320   $aIncludes bibliographical references (p. 193-197) and index.
327   $ach. 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?
330   $aA 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.
606   $aMatrices
608   $aElectronic books.
615  0$aMatrices.
676   $a512.9/434
700   $aBerman$b Abraham$042972
701   $aShaked-Monderer$b Naomi$0906214
801  0$bMiAaPQ
801  1$bMiAaPQ
801  2$bMiAaPQ
906   $aBOOK
912   $a9910454295503321
996   $aCompletely positive matrices$92026800
997   $aUNINA