Softcover ISBN:  9781470463328 
Product Code:  STML/94 
List Price:  $59.00 
Individual Price:  $47.20 
eBook ISBN:  9781470465131 
Product Code:  STML/94.E 
List Price:  $59.00 
Individual Price:  $47.20 
Softcover ISBN:  9781470463328 
eBook: ISBN:  9781470465131 
Product Code:  STML/94.B 
List Price:  $118.00 $88.50 
Softcover ISBN:  9781470463328 
Product Code:  STML/94 
List Price:  $59.00 
Individual Price:  $47.20 
eBook ISBN:  9781470465131 
Product Code:  STML/94.E 
List Price:  $59.00 
Individual Price:  $47.20 
Softcover ISBN:  9781470463328 
eBook ISBN:  9781470465131 
Product Code:  STML/94.B 
List Price:  $118.00 $88.50 

Book DetailsStudent Mathematical LibraryVolume: 94; 2021; 217 ppMSC: 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 MoorePenrose pseudoinverse (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 orientationpreserving 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


Additional Material

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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 MoorePenrose pseudoinverse (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 orientationpreserving 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