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Applied linear algebra and matrix analysis

Author: Thomas S Shores
Publisher: New York : Springer, 2007. ©2007
Series: Undergraduate texts in mathematics; Undergraduate texts in mathematics.
Edition/Format:   Print book : EnglishView all editions and formats
Summary:
"This book offers a fresh approach to matrix and linear algebra by providing a balanced blend of applications, theory, and computation, while highlighting their interdependence. Intended for a one-semester course, Applied Linear Algebra and Matrix Analysis places special emphasis on linear algebra as an experimental science, with numerous examples, computer exercises, and projects. While the flavor is heavily  Read more...
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Details

Genre/Form: Manuels d'enseignement supérieur
Problèmes et exercices
Material Type: Internet resource
Document Type: Book, Internet Resource
All Authors / Contributors: Thomas S Shores
ISBN: 9780387331942 0387331948 9780387331959 0387331956 9780387489476 0387489479
OCLC Number: 71713014
Description: xii, 383 pages : illustrations ; 25 cm.
Contents: 1. Linear systems of equations --
1.1. Some examples --
1.2. Notation and a review of numbers --
1.3. Gaussian elimination: basic ides --
1.4. Gaussian elimination : general procedure --
1.5. *Computational notes and projects --
2. Matrix algebra --
2.1. Matrix addition and scalar multiplication --
2.2. Matrix multiplication --
2.3. Applications of matrix arithmetic --
2.4. Special matrices and transposes --
2.5. Matrix inverses --
2.6. Basic properties of determinants --
2.7. *Computational notes and projects --
3. Vector spaces --
3.1. Definitions and basic concepts --
3.2. Subspaces --
3.3. Linear combinations --
3.4. Subspaces associated with matrices and operators --
3.5. Bases and dimension --
3.6. Linear systems revisited --
3.7. *Computational notes and projects --
4. Geometrical aspects of standard spaces --
4.1. Standard norm and inner product --
4.2. Applications of norms and inner products --
4.3. Orthogonal and unitary matrices --
4.4. *Change of basis and linear operators --
4.5. *Computational notes and projects. 5. The Eigenvalue problem --
5.1. Definitions and basic properties --
5.2. Similarity and diagonalization --
5.3. Applications to discrete dynamical systems --
5.4. Orthogonal diagonalization --
5.5. *Schur form and applications --
5.6. *The singular value decomposition --
5.7. *Computational notes and projects --
6. Geometrical aspects of abstract spaces --
6.1. Normed spaces --
6.2. Inner product spaces --
6.3. Gram-Schmidt algorithm --
6.4. Linear systems revisited --
6.5. *Operator norms --
6.6. *Computational notes and projects --
Table of symbols --
Solutions to selected exercises --
References --
Index.
Series Title: Undergraduate texts in mathematics; Undergraduate texts in mathematics.
Responsibility: Thomas S. Shores.
More information:

Abstract:

This text is intended as a one or two semester sophomore level course in linear algebra. It is designed to provide a balance of applications, theory and computation, and to emphasize their  Read more...

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