Linear Algebra and Matrices

Topics for a Second Course

Helene Shapiro (Autor)

Buch | Hardcover

318 Seiten

2015
American Mathematical Society (Verlag)
978-1-4704-1852-6 (ISBN)

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Linear algebra and matrix theory are fundamental tools for almost every area of mathematics, both pure and applied. This book combines coverage of core topics with an introduction to some areas in which linear algebra plays a key role, for example, block designs, directed graphs, error correcting codes, and linear dynamical systems. Notable features include a discussion of the Weyr characteristic and Weyr canonical forms, and their relationship to the better-known Jordan canonical form; the use of block cyclic matrices and directed graphs to prove Frobenius's theorem on the structure of the eigenvalues of a nonnegative, irreducible matrix; and the inclusion of such combinatorial topics as BIBDs, Hadamard matrices, and strongly regular graphs. Also included are McCoy's theorem about matrices with property P, the Bruck-Ryser-Chowla theorem on the existence of block designs, and an introduction to Markov chains. This book is intended for those who are familiar with the linear algebra covered in a typical first course and are interested in learning more advanced results.

Helene Shapiro, Swarthmore College, PA, USA.

Preliminaries
Inner product spaces and orthogonality
Eigenvalues, eigenvectors, diagonalization, and triangularization
The Jordan and Weyr canonical forms
Unitary similarity and normal matrices
Hermitian matrices
Vector and matrix norms
Some matrix factorizations
Field of values
Simultaneous triangularization
Circulant and block cycle matrices
Matrices of zeros and ones
Block designs
Hadamard matrices
Graphs
Directed graphs
Nonnegative matrices
Error correcting codes
Linear dynamical systems
Bibliography
Index

Reihe/Serie	Pure and Applied Undergraduate Texts
Verlagsort	Providence
Sprache	englisch
Maße	178 x 254 mm
Gewicht	740 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Algebra
	Mathematik / Informatik ► Mathematik ► Geometrie / Topologie
	Mathematik / Informatik ► Mathematik ► Graphentheorie
ISBN-10	1-4704-1852-5 / 1470418525
ISBN-13	978-1-4704-1852-6 / 9781470418526
Zustand	Neuware