Linear algebra in action

Dym offers this graduate-level linear algebra text with a focus on applications. The book begins with a definition of vector spaces and their relationship to matrices. Gaussian elimination and its applications are covered next, followed by eigenvalues, eigenvectors, and determinants. Calculation of Jordan forms is followed by normed linear spaces, inner product spaces, orthogonality, and symmetric, Hermitian, and normal matrices. Singular values, pseudoinverses, triangular factorization, difference equations, and differential equations are covered. Advanced topics included vector-valued functions, the implicit function theorem, extremal problems, matrix-valued holomorphic functions, matrix equations, realization theory, eigenvalue location and zero location problems, convexity, and some special results relating to matrices with nonnegative entries. The second edition is revised for clarity and simplification where possible in some proofs, and includes new short sections on linear programming, extreme points for polyhedra, and a Nevanlinna-Pick interpolation problem.