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Matrix Mathematics: A Second Course in Linear Algebra de Stephan Ramon Garcia

Matrix Mathematics: A Second Course in Linear Algebra: Cambridge Mathematical Textbooks

Autor Stephan Ramon Garcia, Roger A. Horn
en Limba Engleză Hardback – 24 mai 2023
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.
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Specificații

ISBN-13: 9781108837101
ISBN-10: 1108837107
Pagini: 500
Dimensiuni: 183 x 259 x 28 mm
Greutate: 1.06 kg
Ediția:2Revizuită
Editura: Cambridge University Press
Colecția Cambridge University Press
Seria Cambridge Mathematical Textbooks

Locul publicării:New York, United States

Cuprins

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.

Recenzii

'A broad coverage of more advanced topics, rich set of exercises, and thorough index make this stylish book an excellent choice for a second course in linear algebra.' Nick Higham, University of Manchester
'This textbook thoroughly covers all the material you'd expect in a Linear Algebra course plus modern methods and applications. These include topics like the Fourier transform, eigenvalue adjustments, stochastic matrices, interlacing, power method and more. With 20 chapters of such material, this text would be great for a multi-part course and a reference book that all mathematicians should have.' Deanna Needell, University of California, Los Angeles
'The original edition of Garcia and Horn's Second Course in Linear Algebra was well-written, well-organized, and contained several interesting topics that students should see - but rarely do in first-semester linear algebra - such as the singular value decomposition, Gershgorin circles, Cauchy's interlacing theorem, and Sylvester's inertia theorem. This new edition also has all of this, together with useful new material on matrix norms. Any student with the opportunity to take a second course on linear algebra would be lucky to have this book.' Craig Larson, Virginia Commonwealth University
'An extremely versatile Linear Algebra textbook that allows numerous combinations of topics for a traditional course or a more modern and applications-oriented class. Each chapter contains the exact amount of information, presented in a very easy-to-read style, and a plethora of interesting exercises to help the students deepen their knowledge and understanding of the material.' Maria Isabel Bueno Cachadina, University of California, Santa Barbara
'This is an excellent textbook. The topics flow nicely from one chapter to the next and the explanations are very clearly presented. The material can be used for a good second course in Linear Algebra by appropriately choosing the chapters to use. Several options are possible. The breadth of subjects presented makes this book a valuable resource.' Daniel B. Szyld, Temple University and President of the International Linear Algebra Society
'With a careful selection of topics and a deft balance between theory and applications, the authors have created a perfect textbook for a second course on Linear Algebra. The exposition is clear and lively. Rigorous proofs are supplemented by a rich variety of examples, figures, and problems.' Rajendra Bhatia, Ashoka University
'The authors have provided a contemporary, methodical, and clear approach to a broad and comprehensive collection of core topics in matrix theory. They include a wealth of illustrative examples and accompanying exercises to re-enforce the concepts in each chapter. One unique aspect of this book is the inclusion of a large number of concepts that arise in many interesting applications that do not typically appear in other books. I expect this text will be a compelling reference for active researchers and instructors in this subject area.' Shaun Fallat, University of Regina
'It starts from scratch, but manages to cover an amazing variety of topics, of which quite a few cannot be found in standard textbooks. All matrices in the book are over complex numbers, and the connections to physics, statistics, and engineering are regularly highlighted. Compared with the first edition, two new chapters and 300 new problems have been added, as well as many new conceptual examples. Altogether, this is a truly impressive book.' Claus Scheiderer, University of Konstanz

Notă biografică

Descriere

A modern matrix-based approach to a rigorous second course in linear algebra for mathematics, data science, and physical science majors.