This book provides an elementary analytically inclined journey to a fundamental result of linear algebra: the Singular Value Decomposition (SVD). SVD is a workhorse in many applications of linear algebra to data science. Four important applications relevant to data science are considered throughout the book: determining the subspace that "best" approximates a given set (dimension reduction of a data set); finding the "best" lower rank approximation of a given matrix (compression and general approximation problems); the Moore-Penrose pseudo-inverse (relevant to solving least squares problems); and the orthogonal Procrustes problem (finding the orthogonal transformation that most closely transforms a given collection to a given configuration), as well as its orientation-preserving version.The point of view throughout is analytic. Readers are assumed to have had a rigorous introduction to sequences and continuity. These are generalized and applied to linear algebraic ideas. Along the way to the SVD, several important results relevant to a wide variety of fields (including random matrices and spectral graph theory) are explored: the Spectral Theorem; minimax characterizations of eigenvalues; and eigenvalue inequalities. By combining analytic and linear algebraic ideas, readers see seemingly disparate areas interacting in beautiful and applicable ways.
eBook - PDF
Analysis and Linear Algebra: The Singular Value Decomposition and Applications
- 239 pages
- English
- PDF
- Available on iOS & Android
eBook - PDF
Analysis and Linear Algebra: The Singular Value Decomposition and Applications
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Table of contents
- Cover
- Title page
- Copyright
- Contents
- Preface
- Chapter 1. Introduction
- Chapter 2. Linear Algebra and Normed Vector Spaces
- Chapter 3. Main Tools
- Chapter 4. The Spectral Theorem
- Chapter 5. The Singular Value Decomposition
- Chapter 6. Applications Revisited
- Chapter 7. A Glimpse Towards Infinite Dimensions
- Bibliography
- Index of Notation
- Index
- Back Cover
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Yes, you can access Analysis and Linear Algebra: The Singular Value Decomposition and Applications by James Bisgard in PDF and/or ePUB format, as well as other popular books in Mathematics & Mathematics General. We have over one million books available in our catalogue for you to explore.