Matrix Mathematics

Viser: Matrix Mathematics - A Second Course in Linear Algebra

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Matrix Mathematics Vital Source e-bog

Stephan Ramon Garcia og Roger A. Horn

(2023)

Cambridge University Press

773,00 kr.

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A Second Course in Linear Algebra

Stephan Ramon Garcia og Roger A. Horn

(2023)

Sprog: Engelsk

Cambridge University Press

630,00 kr.

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2. Udgave
Vital Source searchable e-book (Fixed pages)
Udgiver: Cambridge University Press (Maj 2023)
Forfattere: Stephan Ramon Garcia og Roger A. Horn
ISBN: 9781108945592

Beskrivelse
Om e-bogen

Using a modern matrix-based approach, this rigorous second course in linear algebra helps upper-level undergraduates in mathematics, data science, and the physical sciences transition from basic theory to advanced topics and applications. Its clarity of exposition together with many illustrations, 900 exercises, and 350 conceptual and numerical examples aid the student's understanding. Concise chapters promote a focused progression through essential ideas. Topics are derived and discussed in detail, including the singular value decomposition, Jordan canonical form, spectral theorem, QR factorization, normal matrices, Hermitian matrices, and positive definite matrices. Each chapter ends with a bullet list summarizing important concepts. New to this edition are chapters on matrix norms and positive matrices, many new sections on topics including interpolation and LU factorization, 300 more problems, many new examples, and color-enhanced figures. Prerequisites include a first course in linear algebra and basic calculus sequence. Instructor's resources are available.

Licens varighed:
Bookshelf online: 5 år fra købsdato.
Bookshelf appen: ubegrænset dage fra købsdato.

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Detaljer om varen

2. Udgave
Hardback: 500 sider
Udgiver: Cambridge University Press (Maj 2023)
Forfattere: Stephan Ramon Garcia og Roger A. Horn
ISBN: 9781108837101

Beskrivelse
Indhold

Using a modern matrix-based approach, this rigorous second course in linear algebra helps upper-level undergraduates in mathematics, data science, and the physical sciences transition from basic theory to advanced topics and applications. Its clarity of exposition together with many illustrations, 900+ exercises, and 350 conceptual and numerical examples aid the student's understanding. Concise chapters promote a focused progression through essential ideas. Topics are derived and discussed in detail, including the singular value decomposition, Jordan canonical form, spectral theorem, QR factorization, normal matrices, Hermitian matrices, and positive definite matrices. Each chapter ends with a bullet list summarizing important concepts. New to this edition are chapters on matrix norms and positive matrices, many new sections on topics including interpolation and LU factorization, 300+ more problems, many new examples, and color-enhanced figures. Prerequisites include a first course in linear algebra and basic calculus sequence. Instructor's resources are available.

Contents; Preface; Notation;
1. Vector Spaces;
2. Bases and Similarity;
3. Block Matrices;
4. Rank, Triangular Factorizations, and Row Equivalence;
5. Inner Products and Norms;
6. Orthonormal Vectors;
7. Unitary Matrices;
8. Orthogonal Complements and Orthogonal Projections;
9. Eigenvalues, Eigenvectors, and Geometric Multiplicity;
10. The Characteristic Polynomial and Algebraic Multiplicity;
11. Unitary Triangularization and Block Diagonalization;
12. The Jordan Form: Existence and Uniqueness;
13. The Jordan Form: Applications;
14. Normal Matrices and the Spectral Theorem;
15. Positive Semidefinite Matrices;
16. The Singular Value and Polar Decompositions;
17. Singular Values and the Spectral Norm;
18. Interlacing and Inertia;
19. Norms and Matrix Norms;
20. Positive and Nonnegative Matrices; References; Index.