Advanced Linear Algebra

• Main Author: Roman, Steven (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: New York, NY : Springer New York, 2005.
• Edition: Second Edition.
• Series: Graduate Texts in Mathematics, 135
• Subjects: Mathematics.; Matrix theory.; Algebra.; Linear and Multilinear Algebras, Matrix Theory.

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...

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.