Frames for Undergraduates
by Han, Deguang
Frames for Undergraduates is an undergraduate-level introduction to the theory of frames in a Hilbert space. This book can serve as a text for a special-topics course in frame theory, but it could also be used to teach a second semester of linear algebra, using frames as an application of the theoretical concepts. It can also provide a complete and helpful resource for students doing undergraduate research projects using frames. The early chapters contain the topics from linear algebra that stu…
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- Full title :Frames for Undergraduates
Summary
Frames for Undergraduates is an undergraduate-level introduction to the theory of frames in a Hilbert space. This book can serve as a text for a special-topics course in frame theory, but it could also be used to teach a second semester of linear algebra, using frames as an application of the theoretical concepts. It can also provide a complete and helpful resource for students doing undergraduate research projects using frames. The early chapters contain the topics from linear algebra that students need to know in order to read the rest of the book. The later chapters are devoted to advanced.
Read More ↓Edition Statements
- Publication Date:2007.
Publication Statements
- Publisher(s):American mathematical Society
- Place of Publication:Providence
- Language:eng
- Publication Date:2007.
Notes
Â10.5. Vandermonde Determinant.
The Physical Object
- Description:1 online resource (314 pages).
Edition Identifiers
- ISBN:9781470421496, 1470421496
- oclc:on1308765559
- LC Classification:QA433.F73 2007
- Dewey Decimal:515/.63
Table of Contents
Cover; Title; Copyright; Contents; Preface for Instructors; Acknowlegements; Introduction; Chapter 1. Linear Algebra Review; Â1.1. Vector Spaces; Â1.2. Bases for Vector Spaces; Â1.3. Linear Operators and Matrices; Â1.4. The Rank of a Linear Operator and a Matrix; Â1.5. Determinant and Trace; Â1.6. Inner Products and Orthonormal Bases; Â1.7. Orthogonal Direct Sum; Â1.8. Exercises from the Text; Â1.9. Additional Exercises; Chapter 2. Finite-Dimensional Operator Theory; Â2.1. Linear Functionals and the Dual Space; Â2.2. Riesz Representation Theorem and Adjoint Operators
Â2.3. Self-adjoint and Unitary OperatorsÂ2.4. Orthogonal Complements and Projections; Â2.5. The Moore-Penrose Inverse; Â2.6. Eigenvalues for Operators; Â2.7. Square Roots of Positive Operators; Â2.8. The Polar Decomposition; Â2.9. Traces of Operators; Â2.10. The Operator Norm; Â2.11. The Spectral Theorem; Â2.12. Exercises from the Text; Â2.13. Additional Exercises; Chapter 3. Introduction to Finite Frames; Â3.1. R[sup(n)]-Frames; Â3.2. Parseval Frames; Â3.3. General Frames and the Canonical Reconstruction Formula; Â3.4. Frames and Matrices
Â3.5. Similarity and Unitary Equivalence of FramesÂ3.6. Frame Potential; Â3.7…
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