Description

Book Synopsis
Presents a user-friendly way the basic and advanced techniques of linear algebra from the point of view of a working analyst. The techniques are illustrated by a wide sample of applications and examples that are chosen to highlight the tools of the trade.

Table of Contents
  • Prerequisites
  • Dimension and rank
  • Gaussian elimination
  • Eigenvalues and eigenvectors
  • Towards the Jordan decomposition
  • The Jordan decomposition
  • Determinants
  • Companion matrices and circulants
  • Inequalities
  • Normed linear spaces
  • Inner product spaces
  • Orthogonality
  • Normal matrices
  • Projections, volumes, and traces
  • Singular value decomposition
  • Positive definite and semidefinite matrices
  • Determinants redux
  • Applications
  • Discrete dynamical systems
  • Continuous dynamical systems
  • Vector-valued functions
  • Fixed point theorems
  • The implicit function theorem
  • Extremal problems
  • Newton's method
  • Matrices with nonnegative entries
  • Applications of matrices with nonnegative entries
  • Eigenvalues of Hermitian matrices
  • Singular values redux I
  • Singular values redux II
  • Approximation by unitary matrices
  • Linear functionals
  • A minimal norm problem
  • Conjugate gradients
  • Continuity of eigenvalues
  • Eigenvalue location problems
  • Matrix equations
  • A matrix completion problem
  • Minimal norm completions
  • The numerical range
  • Riccati equations
  • Supplementary topics
  • Toeplitz, Hankel, and de Branges
  • Bibliography
  • Notation index
  • Subject index.

Linear Algebra in Action

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    Order before 4pm today for delivery by Thu 6 Aug 2026.

    A Paperback by Harry Dym

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      Publisher: American Mathematical Society
      Publication Date: Publication Date: 1/27/2023 12:09:00 AM
      ISBN13: 9781470474195, 978-1470474195
      ISBN10: 1470474190
      Also in:
      Algebraic geometry

      Description

      Book Synopsis
      Presents a user-friendly way the basic and advanced techniques of linear algebra from the point of view of a working analyst. The techniques are illustrated by a wide sample of applications and examples that are chosen to highlight the tools of the trade.

      Table of Contents
      • Prerequisites
      • Dimension and rank
      • Gaussian elimination
      • Eigenvalues and eigenvectors
      • Towards the Jordan decomposition
      • The Jordan decomposition
      • Determinants
      • Companion matrices and circulants
      • Inequalities
      • Normed linear spaces
      • Inner product spaces
      • Orthogonality
      • Normal matrices
      • Projections, volumes, and traces
      • Singular value decomposition
      • Positive definite and semidefinite matrices
      • Determinants redux
      • Applications
      • Discrete dynamical systems
      • Continuous dynamical systems
      • Vector-valued functions
      • Fixed point theorems
      • The implicit function theorem
      • Extremal problems
      • Newton's method
      • Matrices with nonnegative entries
      • Applications of matrices with nonnegative entries
      • Eigenvalues of Hermitian matrices
      • Singular values redux I
      • Singular values redux II
      • Approximation by unitary matrices
      • Linear functionals
      • A minimal norm problem
      • Conjugate gradients
      • Continuity of eigenvalues
      • Eigenvalue location problems
      • Matrix equations
      • A matrix completion problem
      • Minimal norm completions
      • The numerical range
      • Riccati equations
      • Supplementary topics
      • Toeplitz, Hankel, and de Branges
      • Bibliography
      • Notation index
      • Subject index.

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