Linear algebra /

Linear algebra / Michael E. Taylor.

This text develops linear algebra with the view that it is an important gateway connecting elementary mathematics to more advanced subjects, such as advanced calculus, systems of differential equations, differential geometry, and group representations. The purpose of this book is to provide a treatm...

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Bibliographic Details
Online Access: Full Text (via ProQuest)
Main Author: Taylor, Michael E., 1946- (Author)
Format: eBook
Language:English
Published: Providence, Rhode Island : American Mathematical Society, [2020]
Series:Pure and applied undergraduate texts ; 45.
Subjects:
Algebras, Linear.
Table of Contents:
  • Cover
  • Title Page
  • Preface
  • Some basic notation
  • Chapter 1. Vector spaces, linear transformations, and matrices
  • 1.1. Vector spaces
  • 1.2. Linear transformations and matrices
  • 1.3. Basis and dimension
  • 1.4. Matrix representation of a linear transformation
  • 1.5. Determinants and invertibility
  • 1.6. Applications of row reduction and column reduction
  • Chapter 2. Eigenvalues, eigenvectors, and generalized eigenvectors
  • 2.1. Eigenvalues and eigenvectors
  • 2.2. Generalized eigenvectors and the minimal polynomial
  • 2.3. Triangular matrices and upper triangularization.
  • 2.4. The Jordan canonical form
  • Chapter 3. Linear algebra on inner product spaces
  • 3.1. Inner products and norms
  • 3.2. Norm, trace, and adjoint of a linear transformation
  • 3.3. Self-adjoint and skew-adjoint transformations
  • 3.4. Unitary and orthogonal transformations
  • 3.5. Schur's upper triangular representation
  • 3.6. Polar decomposition and singular value decomposition
  • 3.7. The matrix exponential
  • 3.8. The discrete Fourier transform
  • Chapter 4. Further basic concepts: duality, convexity, quotients, positivity
  • 4.1. Dual spaces
  • 4.2. Convex sets
  • 4.3. Quotient spaces.
  • 7.5. Noetherian rings and Noetherian modules
  • 7.6. Polynomial rings over UFDs
  • Chapter 8. Special structures in linear algebra
  • 8.1. Quaternions and matrices of quaternions
  • 8.2. Algebras
  • 8.3. Clifford algebras
  • 8.4. Octonions
  • Appendix A. Complementary results
  • A.1. The fundamental theorem of algebra
  • A.2. Averaging rotations
  • A.3. Groups
  • A.4. Finite fields and other algebraic field extensions
  • Bibliography
  • Index
  • Selected Published Titles in This Series
  • Back Cover.
  • 4.4. Positive matrices and stochastic matrices
  • Chapter 5. Multilinear algebra
  • 5.1. Multilinear mappings
  • 5.2. Tensor products
  • 5.3. Exterior algebra
  • 5.4. Isomorphism kern .5 ( )≈Λ² and the Pfaffian
  • Chapter 6. Linear algebra over more general fields
  • 6.1. Vector spaces over more general fields
  • 6.2. Rational matrices and algebraic numbers
  • Chapter 7. Rings and modules
  • 7.1. Rings and modules
  • 7.2. Modules over principal ideal domains
  • 7.3. The Jordan canonical form revisited
  • 7.4. Integer matrices and algebraic integers.

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