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Advanced Linear Algebra

Steven Roman
Publisher: 
Springer Verlag
Publication Date: 
2007
Number of Pages: 
522
Format: 
Hardcover
Edition: 
3
Series: 
Graduate Texts in Mathematics 135
Price: 
69.95
ISBN: 
9780387728285
Category: 
Textbook
[Reviewed by
Fernando Q. Gouvêa
, on
10/17/2007
]

See Henry Ricardo's review of the second edition. In addition to many local corrections and improvements, the new edition has a new chapter on associative algebras. Included in that chapter are theorems characterizing finite-dimensional division algebras over R and over a finite field. The bibliography has also been enlarged with over a hundred new items.

 

* 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 * Metric Vector Spaces: The Theory of Bilinear Forms * Metric Spaces * Hilbert Spaces * Tensor Products * Positive Solutions to Linear Systems: Convexity and Separation * Affine Geometry * Operator Factorizations: QR and Singular Value * The Umbral Calculus * References * Index

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