Completely positive matrices /:
Annotation
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Weitere Verfasser: | |
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
River Edge, N.J. :
World Scienfic,
2003.
|
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Zusammenfassung: | Annotation |
| Beschreibung: | 1 online resource (ix, 206 pages) : illustrations |
| Bibliographie: | Includes bibliographical references (pages 193-197) and index. |
| ISBN: | 9789812795212 9812795219 9789812383686 9812383689 1281935638 9781281935632 9786611935634 6611935630 |
Internformat
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| 245 | 1 | 0 | |a Completely positive matrices / |c Abraham Berman, Naomi Shaked-Monderer. |
| 260 | |a River Edge, N.J. : |b World Scienfic, |c 2003. | ||
| 300 | |a 1 online resource (ix, 206 pages) : |b illustrations | ||
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| 504 | |a Includes bibliographical references (pages 193-197) and index. | ||
| 588 | 0 | |a Print version record. | |
| 520 | 8 | |a Annotation |b 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 exists, A is called completely positive. The smallest number of columns of a nonnegative matrix B such that A=BBT 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. | |
| 505 | 0 | |a 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? | |
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| 700 | 1 | |a Shaked-Monderer, Naomi. | |
| 758 | |i has work: |a Completely positive matrices (Text) |1 https://id.oclc.org/worldcat/entity/E39PCGBcYc6j4wywfqMyBwqDG3 |4 https://id.oclc.org/worldcat/ontology/hasWork | ||
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| contents | 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? |
| ctrlnum | (OCoLC)263131487 |
| dewey-full | 512.9/434 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512.9/434 |
| dewey-search | 512.9/434 |
| dewey-sort | 3512.9 3434 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Electronic eBook |
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| illustrated | Illustrated |
| indexdate | 2024-11-27T13:16:33Z |
| institution | BVB |
| isbn | 9789812795212 9812795219 9789812383686 9812383689 1281935638 9781281935632 9786611935634 6611935630 |
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| spelling | Berman, Abraham. Completely positive matrices / Abraham Berman, Naomi Shaked-Monderer. River Edge, N.J. : World Scienfic, 2003. 1 online resource (ix, 206 pages) : illustrations text txt rdacontent computer c rdamedia online resource cr rdacarrier data file Includes bibliographical references (pages 193-197) and index. Print version record. Annotation 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 exists, A is called completely positive. The smallest number of columns of a nonnegative matrix B such that A=BBT 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. 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? English. Matrices. http://id.loc.gov/authorities/subjects/sh85082210 Matrices. MATHEMATICS Matrices. bisacsh Matrices fast Matrizes (álgebra) larpcal Shaked-Monderer, Naomi. has work: Completely positive matrices (Text) https://id.oclc.org/worldcat/entity/E39PCGBcYc6j4wywfqMyBwqDG3 https://id.oclc.org/worldcat/ontology/hasWork Print version: Berman, Abraham. Completely positive matrices. River Edge, N.J. : World Scienfic, 2003 9812383689 9789812383686 (DLC) 2004269154 (OCoLC)52718561 FWS01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=235624 Volltext |
| spellingShingle | Berman, Abraham Completely positive matrices / 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? Matrices. http://id.loc.gov/authorities/subjects/sh85082210 Matrices. MATHEMATICS Matrices. bisacsh Matrices fast Matrizes (álgebra) larpcal |
| subject_GND | http://id.loc.gov/authorities/subjects/sh85082210 |
| title | Completely positive matrices / |
| title_auth | Completely positive matrices / |
| title_exact_search | Completely positive matrices / |
| title_full | Completely positive matrices / Abraham Berman, Naomi Shaked-Monderer. |
| title_fullStr | Completely positive matrices / Abraham Berman, Naomi Shaked-Monderer. |
| title_full_unstemmed | Completely positive matrices / Abraham Berman, Naomi Shaked-Monderer. |
| title_short | Completely positive matrices / |
| title_sort | completely positive matrices |
| topic | Matrices. http://id.loc.gov/authorities/subjects/sh85082210 Matrices. MATHEMATICS Matrices. bisacsh Matrices fast Matrizes (álgebra) larpcal |
| topic_facet | Matrices. MATHEMATICS Matrices. Matrices Matrizes (álgebra) |
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