The Linear Algebra a Beginning Graduate Student Ought to Know

Jonathan S. Golan - Collection Kluwer Texts in the Mathematical Sciences

406 pages, parution le 31/01/2004

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Résumé

Linear algebra is a living, active branch of mathematics which is central to almost all other areas of mathematics and which has important applications in all branches of the physical and social sciences and in engineering. However, in recent years the content of linear algebra courses required to complete an undergraduate degree in mathematics -- and even more so in other areas -- at all but the most dedicated universities, has been depleted to the extent that it falls far short of what is in fact needed for graduate study. This is true not only in the areas of theoretical work but also in the areas of computational matrix theory, which are becoming more and more important to the working researcher as personal computers become a common tool. Students are not only less able to formulate or even follow mathematical proofs, they are also less able to understand the underlying mathematics of the numerical algorithms they must use. The resulting knowledge gap has led to frustration and recrimination on the part of both students and faculty alike, with each silently -- and sometimes not so silently -- blaming the other for the resulting state of affairs. This book is written with the intention of bridging that gap. It was designed be used in one or more of several possible ways:

As a reference book;
As a self-study guide;
As a textbook for a course in advanced linear algebra, either at the upper-class undergraduate level or at the first-year graduate level.

The book is self-contained to the extent that it not assume any previous knowledge of linear algebra. It does, however, assume a seriousness of purpose and modicum of mathematical sophistication on the part of the reader. There are almost 1000 exercises, many of them very challenging.

There is a solutions manual to accompany this textbook which is available free to course adopters. If you would like a copy, please e-mail nicole.leblanc@springer-sbm.com

Written for: Textbook for a course in advanced linear algebra, at upper-class undergraduate or first-year graduate level

Sommaire

Notation and Terminology
Fields
Vector Spaces over a Field
Algebras over a Field
Linear Dependence and Dimension
Linear Tranformations
The Endomorphism Algebra of a Vector Space
Representation of Linear Tranformations by Matrices
The Algebra of Square Matrices
Systems of Linear Equations
Determinants
Eigenvalues and Eigenvectors
Krylov Subspaces
The Dual Space
Inner Product Spaces
Orthogonality
Selfadjoint Endomorphisms
Unitary and Normal Endomorphisms
Moore-Penrose Pseudoinverses
Bilinear Transformations and Forms

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	PAPIER
Éditeur(s)	Kluwer Academic Publishers
Auteur(s)	Jonathan S. Golan
Collection	Kluwer Texts in the Mathematical Sciences
Parution	31/01/2004
Nb. de pages	406
Format	16 x 24
Couverture	Relié
Poids	885g
Intérieur	Noir et Blanc
EAN13	9781402018244
ISBN13	978-1-4020-1824-4