Description
Book SynopsisPresents 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.
