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Analysis and Linear Algebra: The Singular Value Decomposition and Applications
 
James Bisgard Central Washington University, Ellensburg, WA
Analysis and Linear Algebra: The Singular Value Decomposition and Applications
Softcover ISBN:  978-1-4704-6332-8
Product Code:  STML/94
List Price: $59.00
Individual Price: $47.20
Sale Price: $35.40
eBook ISBN:  978-1-4704-6513-1
Product Code:  STML/94.E
List Price: $59.00
Individual Price: $47.20
Sale Price: $35.40
Softcover ISBN:  978-1-4704-6332-8
eBook: ISBN:  978-1-4704-6513-1
Product Code:  STML/94.B
List Price: $118.00 $88.50
Sale Price: $70.80 $53.10
Analysis and Linear Algebra: The Singular Value Decomposition and Applications
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Analysis and Linear Algebra: The Singular Value Decomposition and Applications
James Bisgard Central Washington University, Ellensburg, WA
Softcover ISBN:  978-1-4704-6332-8
Product Code:  STML/94
List Price: $59.00
Individual Price: $47.20
Sale Price: $35.40
eBook ISBN:  978-1-4704-6513-1
Product Code:  STML/94.E
List Price: $59.00
Individual Price: $47.20
Sale Price: $35.40
Softcover ISBN:  978-1-4704-6332-8
eBook ISBN:  978-1-4704-6513-1
Product Code:  STML/94.B
List Price: $118.00 $88.50
Sale Price: $70.80 $53.10
  • 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.

  • Table of Contents
     
     
    • 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 publishers of book reviews
    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 publishers of book reviews
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.