Softcover ISBN:  9781470474195 
Product Code:  GSM/232.S 
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eBook ISBN:  9781470474188 
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Softcover ISBN:  9781470474195 
eBook: ISBN:  9781470474188 
Product Code:  GSM/232.S.B 
List Price:  $174.00 $131.50 
MAA Member Price:  $156.60 $118.35 
AMS Member Price:  $139.20 $105.20 
Softcover ISBN:  9781470474195 
Product Code:  GSM/232.S 
List Price:  $89.00 
MAA Member Price:  $80.10 
AMS Member Price:  $71.20 
eBook ISBN:  9781470474188 
Product Code:  GSM/232.E 
List Price:  $85.00 
MAA Member Price:  $76.50 
AMS Member Price:  $68.00 
Softcover ISBN:  9781470474195 
eBook ISBN:  9781470474188 
Product Code:  GSM/232.S.B 
List Price:  $174.00 $131.50 
MAA Member Price:  $156.60 $118.35 
AMS Member Price:  $139.20 $105.20 

Book DetailsGraduate Studies in MathematicsVolume: 232; 2023; 485 ppMSC: Primary 15; 30; 34; 39; 46; 47; 52; 93
This is a Revised Edition of: GSM/78.R
This book is based largely on courses that the author taught at the Feinberg Graduate School of the Weizmann Institute. It conveys in a userfriendly way the basic and advanced techniques of linear algebra from the point of view of a working analyst. The techniques are illustrated by a wide sample of applications and examples that are chosen to highlight the tools of the trade. In short, this is material that the author has found to be useful in his own research and wishes that he had been exposed to as a graduate student.
Roughly the first quarter of the book reviews the contents of a basic course in linear algebra, plus a little. The remaining chapters treat singular value decompositions, convexity, special classes of matrices, projections, assorted algorithms, and a number of applications. The applications are drawn from vector calculus, numerical analysis, control theory, complex analysis, convex optimization, and functional analysis. In particular, fixed point theorems, extremal problems, best approximations, matrix equations, zero location and eigenvalue location problems, matrices with nonnegative entries, and reproducing kernels are discussed.
This new edition differs significantly from the second edition in both content and style. It includes a number of topics that did not appear in the earlier edition and excludes some that did. Moreover, most of the material that has been adapted from the earlier edition has been extensively rewritten and reorganized.
ReadershipUndergraduate and graduate students and researchers interested in learning and teaching linear algebra with an emphasis on concrete algorithms.

Table of Contents

Chapters

Prerequisites

Dimension and rank

Gaussian elimination

Eigenvalues and eigenvectors

Towards the Jordan decomposition

The Jordan decomposition

Determinants

Companion matrices and circulants

Inequalities

Normed linear spaces

Inner product spaces

Orthogonality

Normal matrices

Projections, volumes, and traces

Singular value decomposition

Positive definite and semidefinite matrices

Determinants redux

Applications

Discrete dynamical systems

Continuous dynamical systems

Vectorvalued functions

Fixed point theorems

The implicit function theorem

Extremal problems

Newton’s method

Matrices with nonnegative entries

Applications of matrices with nonnegative entries

Eigenvalues of Hermitian matrices

Singular values redux I

Singular values redux II

Approximation by unitary matrices

Linear functionals

A minimal norm problem

Conjugate gradients

Continuity of eigenvalues

Eigenvalue location problems

Matrix equations

A matrix completion problem

Minimal norm completions

The numerical range

Riccati equations

Supplementary topics

Toeplitz, Hankel, and de Branges


Additional Material

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This is a Revised Edition of: GSM/78.R
This book is based largely on courses that the author taught at the Feinberg Graduate School of the Weizmann Institute. It conveys in a userfriendly way the basic and advanced techniques of linear algebra from the point of view of a working analyst. The techniques are illustrated by a wide sample of applications and examples that are chosen to highlight the tools of the trade. In short, this is material that the author has found to be useful in his own research and wishes that he had been exposed to as a graduate student.
Roughly the first quarter of the book reviews the contents of a basic course in linear algebra, plus a little. The remaining chapters treat singular value decompositions, convexity, special classes of matrices, projections, assorted algorithms, and a number of applications. The applications are drawn from vector calculus, numerical analysis, control theory, complex analysis, convex optimization, and functional analysis. In particular, fixed point theorems, extremal problems, best approximations, matrix equations, zero location and eigenvalue location problems, matrices with nonnegative entries, and reproducing kernels are discussed.
This new edition differs significantly from the second edition in both content and style. It includes a number of topics that did not appear in the earlier edition and excludes some that did. Moreover, most of the material that has been adapted from the earlier edition has been extensively rewritten and reorganized.
Undergraduate and graduate students and researchers interested in learning and teaching linear algebra with an emphasis on concrete algorithms.

Chapters

Prerequisites

Dimension and rank

Gaussian elimination

Eigenvalues and eigenvectors

Towards the Jordan decomposition

The Jordan decomposition

Determinants

Companion matrices and circulants

Inequalities

Normed linear spaces

Inner product spaces

Orthogonality

Normal matrices

Projections, volumes, and traces

Singular value decomposition

Positive definite and semidefinite matrices

Determinants redux

Applications

Discrete dynamical systems

Continuous dynamical systems

Vectorvalued functions

Fixed point theorems

The implicit function theorem

Extremal problems

Newton’s method

Matrices with nonnegative entries

Applications of matrices with nonnegative entries

Eigenvalues of Hermitian matrices

Singular values redux I

Singular values redux II

Approximation by unitary matrices

Linear functionals

A minimal norm problem

Conjugate gradients

Continuity of eigenvalues

Eigenvalue location problems

Matrix equations

A matrix completion problem

Minimal norm completions

The numerical range

Riccati equations

Supplementary topics

Toeplitz, Hankel, and de Branges