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Advanced linear algebra

By: Roman, Steven.
Material type: materialTypeLabelBookSeries: Graduate texts in mathematics: 135.Publisher: New Delhi : Springer, 2007Edition: 3rd ed.Description: xviii, 522 p. ; 25 cm.ISBN: 9788132202974.Subject(s): Algebras, Linear
Contents:
Basic Linear Algebra -- Vector Spaces -- Linear Transformations -- The Isomorphism Theorems -- Modules I: Basic Properties -- Modules II: Free and Noetherian Modules -- Modules over a Principal Ideal Domain -- The Structure of a Linear Operator -- Eigenvalues and Eigenvectors -- Real and Complex Inner Product Spaces -- Structure Theory for Normal Operators -- Topics -- Metric Vector Spaces: The Theory of Bilinear Forms -- Metric Spaces -- Hilbert Spaces -- Tensor Products -- Positive Solutions to Linear Systems: Convexity and Separation -- Affine Geometry -- Singular Values and the Moore-Penrose Inverse -- An Introduction to Algebras -- The Umbral Calculus.
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REF 512.5 MEY-M Matrix analysis and applied linear algebra : REF 512.5 NAI-L Linear algebra REF 512.5 RAO-L Linear algebra REF 512.5 ROM-A Advanced linear algebra REF 512.5 SAI-A Linear algebra REF 512.5 SHI-L Linear algebra REF 512.5 STR-I Introduction to linear algebra

Includes bibliographical references and index.

Pt. I. Basic Linear Algebra -- 1. Vector Spaces -- 2. Linear Transformations -- 3. The Isomorphism Theorems -- 4. Modules I: Basic Properties -- 5. Modules II: Free and Noetherian Modules -- 6. Modules over a Principal Ideal Domain -- 7. The Structure of a Linear Operator -- 8. Eigenvalues and Eigenvectors -- 9. Real and Complex Inner Product Spaces -- 10. Structure Theory for Normal Operators -- Pt. II. Topics -- 11. Metric Vector Spaces: The Theory of Bilinear Forms -- 12. Metric Spaces -- 13. Hilbert Spaces -- 14. Tensor Products -- 15. Positive Solutions to Linear Systems: Convexity and Separation -- 16. Affine Geometry -- 17. Singular Values and the Moore-Penrose Inverse -- 18. An Introduction to Algebras -- 19. The Umbral Calculus.

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