Matrix Theory

From Generalized Inverses to Jordan Form

Robert Piziak, P.L. Odell - Collection Pure and Applied Mathematics

550 pages, parution le 01/03/2007

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Résumé

Focuses on the development of the Moore-Penrose inverse, preparing students for more advanced treatises in matrix theory
Uses concrete examples to make arguments more clear
Presents MATLAB® examples and exercises throughout since it is often used when dealing with matrices
Includes appendices that review basic linear algebra and related prerequisites
Provides numerous homework problems and suggestions for further reading

In 1990, the National Science Foundation recommended that every college mathematics curriculum should include a second course in linear algebra. In answer to this recommendation, Matrix Theory: From Generalized Inverses to Jordan Form provides the material for a second semester of linear algebra that probes introductory linear algebra concepts while also exploring topics not typically covered in a sophomore-level class.

Tailoring the material to advanced undergraduate and beginning graduate students, the authors offer instructors flexibility in choosing topics from the book. The text first focuses on the central problem of linear algebra: solving systems of linear equations. It then discusses LU factorization, derives Sylvester's rank formula, introduces full-rank factorization, and describes generalized inverses. After discussions on norms, QR factorization, and orthogonality, the authors prove the important spectral theorem. They also highlight the primary decomposition theorem, Schur's triangularization theorem, singular value decomposition, and the Jordan canonical form theorem. The book concludes with a chapter on multilinear algebra.

With this classroom-tested text students can delve into elementary linear algebra ideas at a deeper level and prepare for further study in matrix theory and abstract algebra.

Sommaire

The Idea Of Invers
Generating Invertible Matrices
Subspaces Associated To Matrices
The Moore-Penrose Inverse
Generalized Inverses
Norms
Inner Products
Projections
Spectral Theory
Matrix Diagonalization
Jordan Canonical Form
Multilinear Matters

A: Complex numbers
B: Basic matrix operations
C: Determinants
D: A review of basics

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Caractéristiques techniques

	PAPIER
Éditeur(s)	Chapman and Hall / CRC
Auteur(s)	Robert Piziak, P.L. Odell
Collection	Pure and Applied Mathematics
Parution	01/03/2007
Nb. de pages	550
Format	15,5 x 23,5
Couverture	Relié
Poids	895g
Intérieur	Noir et Blanc
EAN13	9781584886259
ISBN13	978-1-58488-625-9