Advanced Linear Algebra
This is a graduate textbook covering an especially broad range of topics. The first part of the book contains a careful but rapid discussion of the basics of linear algebra, including vector spaces, linear transformations, quotient spaces, and isomorphism theorems. The author then proceeds to module...
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| Format: | eBook |
| Language: | English |
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New York, NY
Springer New York
2005, 2005
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| Edition: | 2nd ed. 2005 |
| Series: | Graduate Texts in Mathematics
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| Subjects: | |
| Online Access: | |
| Collection: | Springer eBooks 2005- - Collection details see MPG.ReNa |
Table of Contents:
- Preliminaries
- Preliminaries
- 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
- Operator Factorizations: QR and Singular Value
- The Umbral Calculus