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UID:

Format: 1 Online-Ressource.

Edition: Fourth edition

ISBN: 978-3-031-41026-0

Series Statement: Undergraduate texts in mathematics

Additional Edition: Erscheint auch als Druck-Ausgabe, Hardcover ISBN 978-3-031-41025-3

Additional Edition: Erscheint auch als Druck-Ausgabe, Paperback ISBN 978-3-031-41028-4

Language: English

DOI: 10.1007/978-3-031-41026-0

URL: Volltext  (kostenfrei)

URL: Volltext  (kostenfrei)

Author information: Axler, Sheldon Jay 1949-

UID:

Format: 1 Online-Ressource.

Edition: Fourth edition

ISBN: 978-3-031-41026-0

Series Statement: Undergraduate texts in mathematics

Additional Edition: Erscheint auch als Druck-Ausgabe, Hardcover ISBN 978-3-031-41025-3

Additional Edition: Erscheint auch als Druck-Ausgabe, Paperback ISBN 978-3-031-41028-4

Language: English

DOI: 10.1007/978-3-031-41026-0

URL: Volltext  (kostenfrei)

URL: Volltext  (kostenfrei)

Author information: Axler, Sheldon Jay 1949-

UID:

Format: 1 Online-Ressource

Edition: Fourth edition

ISBN: 9783031410260

Series Statement: Undergraduate texts in mathematics

Additional Edition: Erscheint auch als Druck-Ausgabe, Hardcover ISBN 978-3-031-41025-3

Additional Edition: Erscheint auch als Druck-Ausgabe, Paperback ISBN 978-3-031-41028-4

Language: English

DOI: 10.1007/978-3-031-41026-0

URL: Volltext  (kostenfrei)

URL: Volltext  (kostenfrei)

Author information: Axler, Sheldon Jay 1949-

UID:

Format: 1 online resource (408 pages)

Edition: 4th ed.

ISBN: 9783031410260

Series Statement: Undergraduate Texts in Mathematics Series

Note: Intro -- About the Author -- Contents -- Preface for Students -- Preface for Instructors -- The author's top ten -- Major improvements and additions for the fourth edition -- Acknowledgments -- Chapter 1 Vector Spaces -- 1A Rⁿ and Cⁿ -- Complex Numbers -- Lists -- Fⁿ -- Digression on Fields -- Exercises 1A -- 1B Definition of Vector Space -- Exercises 1B -- 1C Subspaces -- Sums of Subspaces -- Direct Sums -- Exercises 1C -- Chapter 2 Finite-Dimensional Vector Spaces -- 2A Span and Linear Independence -- Linear Combinations and Span -- Linear Independence -- Exercises 2A -- 2B Bases -- Exercises 2B -- 2C Dimension -- Exercises 2C -- Chapter 3 Linear Maps -- 3A Vector Space of Linear Maps -- Definition and Examples of Linear Maps -- Algebraic Operations on L(V, W) -- Exercises 3A -- 3B Null Spaces and Ranges -- Null Space and Injectivity -- Range and Surjectivity -- Fundamental Theorem of Linear Maps -- Exercises 3B -- 3C Matrices -- Representing a Linear Map by a Matrix -- Addition and Scalar Multiplication of Matrices -- Matrix Multiplication -- Column-Row Factorization and Rank of a Matrix -- Exercises 3C -- 3D Invertibility and Isomorphisms -- Invertible Linear Maps -- Isomorphic Vector Spaces -- Linear Maps Thought of as Matrix Multiplication -- Change of Basis -- Exercises 3D -- 3E Products and Quotients of Vector Spaces -- Products of Vector Spaces -- Quotient Spaces -- Exercises 3E -- 3F Duality -- Dual Space and Dual Map -- Null Space and Range of Dual of Linear Map -- Matrix of Dual of Linear Map -- Exercises 3F -- Chapter 4 Polynomials -- Zeros of Polynomials -- Division Algorithm for Polynomials -- Factorization of Polynomials over C -- Factorization of Polynomials over R -- Exercises 4 -- Chapter 5 Eigenvalues and Eigenvectors -- 5A Invariant Subspaces -- Eigenvalues -- Polynomials Applied to Operators -- Exercises 5A. , 5B The Minimal Polynomial -- Existence of Eigenvalues on Complex Vector Spaces -- Eigenvalues and the Minimal Polynomial -- Eigenvalues on Odd-Dimensional Real Vector Spaces -- Exercises 5B -- 5C Upper-Triangular Matrices -- Exercises 5C -- 5D Diagonalizable Operators -- Diagonal Matrices -- Conditions for Diagonalizability -- Gershgorin Disk Theorem -- Exercises 5D -- 5E Commuting Operators -- Exercises 5E -- Chapter 6 Inner Product Spaces -- 6A Inner Products and Norms -- Inner Products -- Norms -- Exercises 6A -- 6B Orthonormal Bases -- Orthonormal Lists and the Gram-Schmidt Procedure -- Linear Functionals on Inner Product Spaces -- Exercises 6B -- 6C Orthogonal Complements and Minimization Problems -- Orthogonal Complements -- Minimization Problems -- Pseudoinverse -- Exercises 6C -- Chapter 7 Operators on Inner Product Spaces -- 7A Self-Adjoint and Normal Operators -- Adjoints -- Self-Adjoint Operators -- Normal Operators -- Exercises 7A -- 7B Spectral Theorem -- Real Spectral Theorem -- Complex Spectral Theorem -- Exercises 7B -- 7C Positive Operators -- Exercises 7C -- 7D Isometries, Unitary Operators, and Matrix Factorization -- Isometries -- Unitary Operators -- QR Factorization -- Cholesky Factorization -- Exercises 7D -- 7E Singular Value Decomposition -- Singular Values -- SVD for Linear Maps and for Matrices -- Exercises 7E -- 7F Consequences of Singular Value Decomposition -- Norms of Linear Maps -- Approximation by Linear Maps with Lower-Dimensional Range -- Polar Decomposition -- Operators Applied to Ellipsoids and Parallelepipeds -- Volume via Singular Values -- Properties of an Operator as Determined by Its Eigenvalues -- Exercises 7F -- Chapter 8 Operators on Complex Vector Spaces -- 8A Generalized Eigenvectors and Nilpotent Operators -- Null Spaces of Powers of an Operator -- Generalized Eigenvectors -- Nilpotent Operators. , Exercises 8A -- 8B Generalized Eigenspace Decomposition -- Generalized Eigenspaces -- Multiplicity of an Eigenvalue -- Block Diagonal Matrices -- Exercises 8B -- 8C Consequences of Generalized Eigenspace Decomposition -- Square Roots of Operators -- Jordan Form -- Exercises 8C -- 8D Trace: A Connection Between Matrices and Operators -- Exercises 8D -- Chapter 9 Multilinear Algebra and Determinants -- 9A Bilinear Forms and Quadratic Forms -- Bilinear Forms -- Symmetric Bilinear Forms -- Quadratic Forms -- Exercises 9A -- 9B Alternating Multilinear Forms -- Multilinear Forms -- Alternating Multilinear Forms and Permutations -- Exercises 9B -- 9C Determinants -- Defining the Determinant -- Properties of Determinants -- Exercises 9C -- 9D Tensor Products -- Tensor Product of Two Vector Spaces -- Tensor Product of Inner Product Spaces -- Tensor Product of Multiple Vector Spaces -- Exercises 9D -- Photo Credits -- Symbol Index -- Index -- Colophon: Notes on Typesetting.

Additional Edition: Print version: Axler, Sheldon Linear Algebra Done Right Cham : Springer International Publishing AG,c2023

Language: English

Keywords: Electronic books. ; Electronic books.

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URL: Click here to view book

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UID:

Format: 1 online resource (408 pages)

Edition: 4th ed. 2024.

ISBN: 3-031-41026-2

Series Statement: Undergraduate Texts in Mathematics,

Content: Now available in Open Access, this best-selling textbook for a second course in linear algebra is aimed at undergraduate math majors and graduate students. The fourth edition gives an expanded treatment of the singular value decomposition and its consequences. It includes a new chapter on multilinear algebra, treating bilinear forms, quadratic forms, tensor products, and an approach to determinants via alternating multilinear forms. This new edition also increases the use of the minimal polynomial to provide cleaner proofs of multiple results. Also, over 250 new exercises have been added. The novel approach taken here banishes determinants to the end of the book. The text focuses on the central goal of linear algebra: understanding the structure of linear operators on finite-dimensional vector spaces. The author has taken unusual care to motivate concepts and simplify proofs. A variety of interesting exercises in each chapter helps students understand and manipulate the objects of linear algebra. Beautiful formatting creates pages with an unusually student-friendly appearance in both print and electronic versions. No prerequisites are assumed other than the usual demand for suitable mathematical maturity. The text starts by discussing vector spaces, linear independence, span, basis, and dimension. The book then deals with linear maps, eigenvalues, and eigenvectors. Inner-product spaces are introduced, leading to the finite-dimensional spectral theorem and its consequences. Generalized eigenvectors are then used to provide insight into the structure of a linear operator. From reviews of previous editions: Altogether, the text is a didactic masterpiece. — zbMATH The determinant-free proofs are elegant and intuitive. — American Mathematical Monthly The most original linear algebra book to appear in years, it certainly belongs in every undergraduate library — CHOICE.

Note: Preface for the Instructor-Preface for the Student-Acknowledgments-1. Vector Spaces -- 2. Finite-Dimensional Vector Spaces -- 3. Linear Maps -- 4. Polynomials -- 5. Eigenvalues, Eigenvectors, and Invariant Subspaces -- 6. Inner Product Spaces -- 7. Operators on Inner Product Spaces -- 8. Operators on Complex Vector Spaces -- 9. Operators on Real Vector Spaces -- 10. Trace and Determinant-Photo Credits-Symbol Index-Index.

Additional Edition: ISBN 3-031-41025-4

Language: English

DOI: 10.1007/978-3-031-41026-0

UID:

Format: 1 Online-Ressource (390 p.)

ISBN: 9783031410260 , 9783031410253

Series Statement: Undergraduate Texts in Mathematics

Content: Now available in Open Access, this best-selling textbook for a second course in linear algebra is aimed at undergraduate math majors and graduate students. The fourth edition gives an expanded treatment of the singular value decomposition and its consequences. It includes a new chapter on multilinear algebra, treating bilinear forms, quadratic forms, tensor products, and an approach to determinants via alternating multilinear forms. This new edition also increases the use of the minimal polynomial to provide cleaner proofs of multiple results. Also, over 250 new exercises have been added. The novel approach taken here banishes determinants to the end of the book. The text focuses on the central goal of linear algebra: understanding the structure of linear operators on finite-dimensional vector spaces. The author has taken unusual care to motivate concepts and simplify proofs. A variety of interesting exercises in each chapter helps students understand and manipulate the objects of linear algebra. Beautiful formatting creates pages with an unusually student-friendly appearance in both print and electronic versions. No prerequisites are assumed other than the usual demand for suitable mathematical maturity. The text starts by discussing vector spaces, linear independence, span, basis, and dimension. The book then deals with linear maps, eigenvalues, and eigenvectors. Inner-product spaces are introduced, leading to the finite-dimensional spectral theorem and its consequences. Generalized eigenvectors are then used to provide insight into the structure of a linear operator. From the reviews of previous editions: Altogether, the text is a didactic masterpiece. — zbMATH The determinant-free proofs are elegant and intuitive. — American Mathematical Monthly The most original linear algebra book to appear in years, it certainly belongs in every undergraduate library — CHOICE

Note: English

Language: Undetermined

URL: kostenfrei

UID:

Format: 1 online resource (408 pages)

Edition: 4th ed. 2024.

ISBN: 3-031-41026-2

Series Statement: Undergraduate Texts in Mathematics,

Content: Now available in Open Access, this best-selling textbook for a second course in linear algebra is aimed at undergraduate math majors and graduate students. The fourth edition gives an expanded treatment of the singular value decomposition and its consequences. It includes a new chapter on multilinear algebra, treating bilinear forms, quadratic forms, tensor products, and an approach to determinants via alternating multilinear forms. This new edition also increases the use of the minimal polynomial to provide cleaner proofs of multiple results. Also, over 250 new exercises have been added. The novel approach taken here banishes determinants to the end of the book. The text focuses on the central goal of linear algebra: understanding the structure of linear operators on finite-dimensional vector spaces. The author has taken unusual care to motivate concepts and simplify proofs. A variety of interesting exercises in each chapter helps students understand and manipulate the objects of linear algebra. Beautiful formatting creates pages with an unusually student-friendly appearance in both print and electronic versions. No prerequisites are assumed other than the usual demand for suitable mathematical maturity. The text starts by discussing vector spaces, linear independence, span, basis, and dimension. The book then deals with linear maps, eigenvalues, and eigenvectors. Inner-product spaces are introduced, leading to the finite-dimensional spectral theorem and its consequences. Generalized eigenvectors are then used to provide insight into the structure of a linear operator. From reviews of previous editions: Altogether, the text is a didactic masterpiece. — zbMATH The determinant-free proofs are elegant and intuitive. — American Mathematical Monthly The most original linear algebra book to appear in years, it certainly belongs in every undergraduate library — CHOICE.

Note: Preface for the Instructor-Preface for the Student-Acknowledgments-1. Vector Spaces -- 2. Finite-Dimensional Vector Spaces -- 3. Linear Maps -- 4. Polynomials -- 5. Eigenvalues, Eigenvectors, and Invariant Subspaces -- 6. Inner Product Spaces -- 7. Operators on Inner Product Spaces -- 8. Operators on Complex Vector Spaces -- 9. Operators on Real Vector Spaces -- 10. Trace and Determinant-Photo Credits-Symbol Index-Index.

Additional Edition: ISBN 3-031-41025-4

Language: English

DOI: 10.1007/978-3-031-41026-0

UID:

Format: 1 online resource (408 pages)

Edition: 4th ed. 2024.

ISBN: 3-031-41026-2

Series Statement: Undergraduate Texts in Mathematics,

Content: Now available in Open Access, this best-selling textbook for a second course in linear algebra is aimed at undergraduate math majors and graduate students. The fourth edition gives an expanded treatment of the singular value decomposition and its consequences. It includes a new chapter on multilinear algebra, treating bilinear forms, quadratic forms, tensor products, and an approach to determinants via alternating multilinear forms. This new edition also increases the use of the minimal polynomial to provide cleaner proofs of multiple results. Also, over 250 new exercises have been added. The novel approach taken here banishes determinants to the end of the book. The text focuses on the central goal of linear algebra: understanding the structure of linear operators on finite-dimensional vector spaces. The author has taken unusual care to motivate concepts and simplify proofs. A variety of interesting exercises in each chapter helps students understand and manipulate the objects of linear algebra. Beautiful formatting creates pages with an unusually student-friendly appearance in both print and electronic versions. No prerequisites are assumed other than the usual demand for suitable mathematical maturity. The text starts by discussing vector spaces, linear independence, span, basis, and dimension. The book then deals with linear maps, eigenvalues, and eigenvectors. Inner-product spaces are introduced, leading to the finite-dimensional spectral theorem and its consequences. Generalized eigenvectors are then used to provide insight into the structure of a linear operator. From reviews of previous editions: Altogether, the text is a didactic masterpiece. — zbMATH The determinant-free proofs are elegant and intuitive. — American Mathematical Monthly The most original linear algebra book to appear in years, it certainly belongs in every undergraduate library — CHOICE.

Note: Preface for the Instructor-Preface for the Student-Acknowledgments-1. Vector Spaces -- 2. Finite-Dimensional Vector Spaces -- 3. Linear Maps -- 4. Polynomials -- 5. Eigenvalues, Eigenvectors, and Invariant Subspaces -- 6. Inner Product Spaces -- 7. Operators on Inner Product Spaces -- 8. Operators on Complex Vector Spaces -- 9. Operators on Real Vector Spaces -- 10. Trace and Determinant-Photo Credits-Symbol Index-Index.

Additional Edition: ISBN 3-031-41025-4

Language: English

DOI: 10.1007/978-3-031-41026-0

UID:

Format: 1 online resource (408 pages)

Edition: 4th ed. 2024.

ISBN: 3-031-41026-2

Series Statement: Undergraduate Texts in Mathematics,

Content: Now available in Open Access, this best-selling textbook for a second course in linear algebra is aimed at undergraduate math majors and graduate students. The fourth edition gives an expanded treatment of the singular value decomposition and its consequences. It includes a new chapter on multilinear algebra, treating bilinear forms, quadratic forms, tensor products, and an approach to determinants via alternating multilinear forms. This new edition also increases the use of the minimal polynomial to provide cleaner proofs of multiple results. Also, over 250 new exercises have been added. The novel approach taken here banishes determinants to the end of the book. The text focuses on the central goal of linear algebra: understanding the structure of linear operators on finite-dimensional vector spaces. The author has taken unusual care to motivate concepts and simplify proofs. A variety of interesting exercises in each chapter helps students understand and manipulate the objects of linear algebra. Beautiful formatting creates pages with an unusually student-friendly appearance in both print and electronic versions. No prerequisites are assumed other than the usual demand for suitable mathematical maturity. The text starts by discussing vector spaces, linear independence, span, basis, and dimension. The book then deals with linear maps, eigenvalues, and eigenvectors. Inner-product spaces are introduced, leading to the finite-dimensional spectral theorem and its consequences. Generalized eigenvectors are then used to provide insight into the structure of a linear operator. From reviews of previous editions: Altogether, the text is a didactic masterpiece. — zbMATH The determinant-free proofs are elegant and intuitive. — American Mathematical Monthly The most original linear algebra book to appear in years, it certainly belongs in every undergraduate library — CHOICE.

Note: Preface for the Instructor-Preface for the Student-Acknowledgments-1. Vector Spaces -- 2. Finite-Dimensional Vector Spaces -- 3. Linear Maps -- 4. Polynomials -- 5. Eigenvalues, Eigenvectors, and Invariant Subspaces -- 6. Inner Product Spaces -- 7. Operators on Inner Product Spaces -- 8. Operators on Complex Vector Spaces -- 9. Operators on Real Vector Spaces -- 10. Trace and Determinant-Photo Credits-Symbol Index-Index.

Additional Edition: ISBN 3-031-41025-4

Language: English

DOI: 10.1007/978-3-031-41026-0

UID:

Format: XVII, 390 p. 33 illus. in color. , online resource.

Edition: 4th ed. 2024.

ISBN: 9783031410260

Series Statement: Undergraduate Texts in Mathematics,

Content: Now available in Open Access, this best-selling textbook for a second course in linear algebra is aimed at undergraduate math majors and graduate students. The fourth edition gives an expanded treatment of the singular value decomposition and its consequences. It includes a new chapter on multilinear algebra, treating bilinear forms, quadratic forms, tensor products, and an approach to determinants via alternating multilinear forms. This new edition also increases the use of the minimal polynomial to provide cleaner proofs of multiple results. Also, over 250 new exercises have been added. The novel approach taken here banishes determinants to the end of the book. The text focuses on the central goal of linear algebra: understanding the structure of linear operators on finite-dimensional vector spaces. The author has taken unusual care to motivate concepts and simplify proofs. A variety of interesting exercises in each chapter helps students understand and manipulate the objects of linear algebra. Beautiful formatting creates pages with an unusually student-friendly appearance in both print and electronic versions. No prerequisites are assumed other than the usual demand for suitable mathematical maturity. The text starts by discussing vector spaces, linear independence, span, basis, and dimension. The book then deals with linear maps, eigenvalues, and eigenvectors. Inner-product spaces are introduced, leading to the finite-dimensional spectral theorem and its consequences. Generalized eigenvectors are then used to provide insight into the structure of a linear operator. From reviews of previous editions: Altogether, the text is a didactic masterpiece. - zbMATH The determinant-free proofs are elegant and intuitive. - American Mathematical Monthly The most original linear algebra book to appear in years, it certainly belongs in every undergraduate library - CHOICE.

Note: Preface for the Instructor-Preface for the Student-Acknowledgments-1. Vector Spaces -- 2. Finite-Dimensional Vector Spaces -- 3. Linear Maps -- 4. Polynomials -- 5. Eigenvalues, Eigenvectors, and Invariant Subspaces -- 6. Inner Product Spaces -- 7. Operators on Inner Product Spaces -- 8. Operators on Complex Vector Spaces -- 9. Operators on Real Vector Spaces -- 10. Trace and Determinant-Photo Credits-Symbol Index-Index.

In: Springer Nature eBook

Additional Edition: Printed edition: ISBN 9783031410253

Additional Edition: Printed edition: ISBN 9783031410277

Additional Edition: Printed edition: ISBN 9783031410284

Language: English

DOI: 10.1007/978-3-031-41026-0

URL: https://doi.org/10.1007/978-3-031-41026-0