Special matrices and their applications in numerical mathematics - Hardcover

Miroslav Fiedler

Hardcover

ISBN 10: 9024729572 ISBN 13: 9789024729579

Publisher: Springer, 1633

Synopsis

This is an updated translation of a book published in Czech by the SNTL - Publishers of Technical Literature in 1981. In developing this book, it was found reasonable to consider special matrices in general sense and also to include some more or less auxiliary topics that made it possible to present some facts or processes more demonstratively. An example is the graph theory. Chapter 1 contains the definitions of basic concepts of the theory of matrices, and fundamental theorems. The Schur complement is defined here in full generality and using its properties we prove the theorem on the factorization of a partitioned matrix into the product of a lower block triangular matrix with identity diagonal blocks, a block diagonal matrix, and an upper block triangular matrix with identity diagonal blocks. The theorem on the Jordan normal form of a matrix is gi¥en without proof. Chapter 2 is concerned with symmetric and Hermitian matrices. We prove Schur's theorem and, using it, we establish the fundamental theorem describing the factorization of symmetric or Hermitian matrices. Further, the properties of positive definite and positive semidefinite matrices are studied. In the conclusion, Sylvester's law of inertia of quadratic forms and theorems on the singular value decomposition and polar decomposition are proved. Chapter 3 treats the mutual connections between graphs and matrices.

About this title

Language Notes:

Text: English, Czech (translation)

About this edition

• Publisher: Springer
• Publication date: 1633
• ISBN 10: 9024729572
• ISBN 13: 9789024729579
• Binding: Hardcover
• Edition number: 1
• Number of pages: 308