http://www.loc.gov/mods/v3 http://www.loc.gov/standards/mods/v3/mods-3-2.xsd
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
Includes bibliographical references and indexes.
Linear and multilinear algebra; matrix theory -- Instructional exposition (textbooks, tutorial papers, etc.)
Functions of a complex variable -- Instructional exposition (textbooks, tutorial papers, etc.)
Ordinary differential equations -- Instructional exposition (textbooks, tutorial papers, etc.)
Difference and functional equations -- Instructional exposition (textbooks, tutorial papers, etc.)
Functional analysis -- Linear function spaces and their duals -- Hilbert spaces with reproducing kernels (= [proper] functional Hilbert spaces, including de Branges-Rovnyak and other structured spaces
Operator theory -- Special classes of linear operators -- Operators in reproducing-kernel Hilbert spaces (including de Branges, de Branges-Rovnyak, and other structured spaces)
Convex and discrete geometry -- Instructional exposition (textbooks, tutorial papers, etc.)
Systems theory; control -- Instructional exposition (textbooks, tutorial papers, etc.)
Providence, Rhode Island : American Mathematical Society, [2023]
Graduate studies in mathematics ; v. 232