Matrix mathematics : a second course in linear algebra

著者

書誌事項

Matrix mathematics : a second course in linear algebra

Stephan Ramon Garcia, Roger A. Horn

（Cambridge mathematical textbooks）

Cambridge University Press, 2023

2nd ed

大学図書館所蔵 件 / 全4件

この図書・雑誌をさがす

注記

Previous ed.: 2017

Includes bibliographical references and index

内容説明・目次

内容説明

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.

目次

  • 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.

「Nielsen BookData」 より

関連文献： 1件中  1-1を表示

詳細情報

ページトップへ