Completely positive matrices /
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| Author / Creator: | Berman, Abraham. |
|---|---|
| Imprint: | [River Edge] New Jersey : World Scientific, c2003. |
| Description: | ix, 206 p. ; 24 cm. |
| Language: | English |
| Subject: | |
| Format: | Print Book |
| URL for this record: | http://pi.lib.uchicago.edu/1001/cat/bib/4966390 |
Table of Contents:
- Preface
- Chapter 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
- Chapter 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
- Chapter 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?
- Bibliography
- Notation
- Index
