Introduction to Linear Algebra

Höfundur: Frank M. Stewart (Útgáfa: 0)
Introduction to Linear Algebra

Kaup valmöguleikar

Introduction to Linear Algebra stresses finite dimensional vector spaces and linear transformations. Intended for undergraduate majors in mathematics, applied mathematics, chemistry, and physics, the treatment's only prerequisite is a first course in calculus. Proofs are given in detail, and carefully chosen problems demonstrate the variety of situations in which these concepts arise. After a brief Introduction, the text advances to chapters on the plane, linear dependence, span, dimension, bases, and subspaces.

Nánar um bókina

Útgefandi
Dover Publications
ISBN
9780486841519
Print ISBN
9780486834122
Format
ePub
Útgáfa
0
Höfundar
Frank M. Stewart
Tungumál
English
Útgefið
2019-07-17
Prent takmörkun á líftíma
100

Kaflar

  • Cover
  • Title Page
  • Copyright Page
  • Dedication
  • Contents
  • Preface
  • Note to the Reader
  • Chapter I Introduction
  • 1. An Example
  • 2. Further Examples
  • 3. Elementary Properties
  • 4. Problems
  • Summary
  • Chapter II The PLANE
  • 5. Dimension, Bases
  • 6. Distance and Inner Products
  • 7. Some Geometry
  • 8. Area
  • 9. Problems
  • Summary
  • Chapter III Linear Dependence, Span, Dimension, Bases, Subspaces
  • 10. Linear Dependence and Independence
  • 11. Dimension
  • 12. Bases
  • 13. Subspaces
  • 14. Problems
  • Summary
  • Chapter IV Linear Transformations
  • 15. Linear Transformations
  • 16. The Algebra of Transformations
  • 17. Simultaneous Linear Equations: General Theory
  • 18. Simultaneous Linear Equations: Computation
  • 19. Matrices
  • 20. Problems
  • Summary
  • Chapter V The Dual Space; Multilinear Forms; Determinants
  • 21. Linear Functionals and the Dual Space
  • 22. Multilinear Forms
  • 23. Determinants of Linear Transformations
  • 24. Determinants of Matrices
  • 25. Problems
  • Summary
  • Chapter VI Determinants: A Traditional Treatment
  • 26. Permutations
  • 27. Determinants
  • 28. Expansion by Minors
  • 29. The Determinant of a Product
  • 30. The Determinant of a Linear Transformation
  • 31. Problems
  • Summary
  • Chapter VII Inner Product Spaces
  • 32. Inner Products
  • 33. Norms and Orthogonality
  • 34. Orthonormal Bases
  • 35. Eigenvalues
  • 36. Symmetric Transformations
  • 37. The Spectral Theorem
  • 38. Problems
  • Summary
  • Appendix A. Equations and Identities
  • Appendix B. Variables and Quantifiers, Unknowns
  • Appendix C. Sets
  • Appendix D. Proofs
  • Appendix E. Indices and Summation
  • Appendix F. Functions
  • Index of Symbols
  • Index
  • List of Definitions, Theorems, Corollaries, and Lemmas