Matrix Mathematics

A Second Course in Linear Algebra
2. Auflage 2023
ISBN: 978-1-108-83710-1
Verlag: Cambridge University Pr.

Buch, Englisch, 500 Seiten, Format (B × H): 180 mm x 258 mm, Gewicht: 1138 g

Reihe: Cambridge Mathematical Textbooks

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.

Autoren/Hrsg.

Garcia, Stephan Ramon

Horn, Roger A

Fachgebiete

• Mathematik | Informatik Mathematik Algebra

Inhaltsverzeichnis

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.

Über Autor(innen)

Garcia, Stephan Ramon
Stephan Ramon Garcia is W.M. Keck Distinguished Service Professor and Chair of the Department of Mathematics and Statistics at Pomona College. He is the author of five books and over 100 research articles in operator theory, complex analysis, matrix analysis, number theory, discrete geometry, and combinatorics. He has served on the editorial boards of the Proceedings of the American Mathematical Society, Notices of the American Mathematical Society, Involve, and The American Mathematical Monthly. He received six teaching awards from three different institutions and is a fellow of the American Mathematical Society, which has awarded him the inaugural Dolciani Prize for Excellence in Research.

Horn, Roger A
Roger A. Horn was Professor and Chair of the Department of Mathematical Sciences at the Johns Hopkins University, and Research Professor of Mathematics at the University of Utah until his retirement in 2015. His publications include Matrix Analysis, 2nd edition (Cambridge, 2012) and Topics in Matrix Analysis (with Charles R. Johnson, Cambridge, 1991), as well as more than 100 research articles in matrix analysis, statistics, health services research, complex variables, probability, differential geometry, and analytic number theory. He was the editor of The American Mathematical Monthly and has served on the editorial boards of the SIAM Journal of Matrix Analysis, Linear Algebra and its Applications, and the Electronic Journal of Linear Algebra.