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Analysis and Linear Algebra : The Singular Value Decomposition and Applications, Paperback / softback Book

Analysis and Linear Algebra : The Singular Value Decomposition and Applications Paperback / softback

Part of the Student Mathematical Library series

Paperback / softback

Available to Order - This title is available to order, with delivery expected within 2 weeks

Description

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.

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£52.00

Available to Order - This title is available to order, with delivery expected within 2 weeks
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