Matrix Algebra

2007
ISBN: 978-0-387-70872-0
Verlag: Springer

Buch, Englisch, 530 Seiten, Format (B × H): 155 mm x 235 mm, Gewicht: 2100 g

Reihe: Springer Texts in Statistics

Matrix algebra is one of the most important areas of mathematics for data analysis and for statistical theory. This much-needed work presents the relevant aspects of the theory of matrix algebra for applications in statistics. It moves on to consider the various types of matrices encountered in statistics, such as projection matrices and positive definite matrices, and describes the special properties of those matrices. Finally, it covers numerical linear algebra, beginning with a discussion of the basics of numerical computations, and following up with accurate and efficient algorithms for factoring matrices, solving linear systems of equations, and extracting eigenvalues and eigenvectors.

Zielgruppe

Research

Autoren/Hrsg.

Gentle, James E.

Fachgebiete

• Mathematik | Informatik Mathematik Stochastik Mathematische Statistik
• Mathematik | Informatik Mathematik Algebra Lineare und multilineare Algebra, Matrizentheorie
• Mathematik | Informatik EDV | Informatik Informatik Mathematik für Informatiker
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen

Inhaltsverzeichnis

Linear Algebra.- Basic Vector/Matrix Structure and Notation.- Vectors and Vector Spaces.- Basic Properties of Matrices.- Vector/Matrix Derivatives and Integrals.- Matrix Transformations and Factorizations.- Solution of Linear Systems.- Evaluation of Eigenvalues and Eigenvectors.- Applications in Data Analysis.- Special Matrices and Operations Useful in Modeling and Data Analysis.- Selected Applications in Statistics.- Numerical Methods and Software.- Numerical Methods.- Numerical Linear Algebra.- Software for Numerical Linear Algebra.