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Analysis and Linear Algebra: The Singular Value Decomposition and Applications

James Bisgard Central Washington University, Ellensburg, WA
Available Formats:
Softcover ISBN: 978-1-4704-6332-8
Product Code: STML/94
List Price: $59.00 Individual Price:$47.20
Electronic ISBN: 978-1-4704-6513-1
Product Code: STML/94.E
List Price: $59.00 Individual Price:$47.20
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List Price: $88.50 Click above image for expanded view Analysis and Linear Algebra: The Singular Value Decomposition and Applications James Bisgard Central Washington University, Ellensburg, WA Available Formats:  Softcover ISBN: 978-1-4704-6332-8 Product Code: STML/94  List Price:$59.00 Individual Price: $47.20  Electronic ISBN: 978-1-4704-6513-1 Product Code: STML/94.E  List Price:$59.00 Individual Price: $47.20 Bundle Print and Electronic Formats and Save! This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version.  List Price:$88.50
• Book Details

Student Mathematical Library
Volume: 942021; 217 pp
MSC: Primary 15; 26; 49;

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.

• Chapters
• Introduction
• Linear algebra and normed vector spaces
• Main tools
• The spectral theorem
• The singular value decomposition
• Applications revisited
• A glimpse towards infinite dimensions

• Requests

Review Copy – for reviewers who would like to review an AMS book
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
Volume: 942021; 217 pp
MSC: Primary 15; 26; 49;

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.

• Chapters
• Introduction
• Linear algebra and normed vector spaces
• Main tools
• The spectral theorem
• The singular value decomposition
• Applications revisited
• A glimpse towards infinite dimensions
Review Copy – for reviewers who would like to review an AMS book
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
Please select which format for which you are requesting permissions.