|Seber, George A. F.|
A Matrix Handbook for Statisticians
Wiley Series in Probability and Statistics
1. Auflage Dezember 2007
2007. 560 Seiten, Hardcover
ISBN 978-0-471-74869-4 - John Wiley & Sons
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A Matrix Handbook for Statisticians emphasizes computational statistics and algorithms due to the growing need for more modern techniques and includes numerous references to both the theory behind the methods and the applications of the methods. It's unique because of its extensive cross-referencing of topics within the book as well as external referencing for proofs. Each chapter consists of four parts: a definition followed by a list of results, a short list of references to related topics in the book (since some overlap is unavoidable), one or more references to proofs, and references to applications. Dr. Seber, a highly qualified authority on matrix theory, is the ideal choice for authoring a handbook on matrices. His approach provides comprehensive coverage of the matrix theory and includes a collection of topics not found in any other one book.
Aus dem Inhalt
2. Vectors, Vector Spaces, and Convexity.
4. Matrix Functions: Inverse, Transpose, Trace, Determinant, and Norm.
5. Complex, Hermitian, and Related Matrices.
6. Eigenvalues, Eigenvectors, and Singular Values.
7. Generalized Inverses.
8. Some Special Matrices.
9. Non-Negative Vectors and Matrices.
10. Positive Definite and Non-negative Definite Matrices.
11. Special Products and Operators.
13. Linear Equations.
14. Partitioned Matrices.
15. Patterned Matrices.
16. Factorization of Matrices.
17. Differentiation and Finite Differences.
19. Matrix Limits, Sequences and Series.
20. Random Vectors.
21. Random Matrices.
22. Inequalities for Probabilities and Random Variables.
24. Optimization and Matrix Approximation.