Author | Gohberg, Israel. author |
---|---|
Title | Partially Specified Matrices and Operators: Classification, Completion, Applications [electronic resource] / by Israel Gohberg, Marinus A. Kaashoek, Frederik van Schagen |
Imprint | Basel : Birkhรคuser Basel, 1995 |
Connect to | http://dx.doi.org/10.1007/978-3-0348-9100-4 |
Descript | 368 p. online resource |
I. Main problems and motivation -- I.1 Eigenvalue completion problems and first examples -- I.2 Reduction by similarity -- I.3 Blocks -- I.4 Block similarity -- I.5 Special cases of block similarity -- I.6 Eigenvalue completion and restriction problems -- Notes -- II. Elementary operations on blocks -- II.1 Block-invariant subspaces -- II.2 Direct sums of blocks and decomposable blocks -- II.3 Indecomposable blocks -- II.4 Duality of blocks -- Notes -- III. Full length blocks -- III.1 Structure theorems for full length blocks -- III.2 Finite dimensional operator pencils -- III.3 Similarity of non-everywhere defined linear operators -- III.4 Dual sequences -- Notes -- IV. The eigenvalue completion problem for full length blocks -- IV.1 Main theorems -- IV.2 Reduction to a problem on matrix polynomials -- IV.3 A one column completion problem for matrix polynomials -- IV.4 Proof of the first main theorem -- IV.5 Some applications of the restriction problem -- IV.6 A matrix equation -- Notes -- V. Full width blocks -- V.1 Structure theorems for full width blocks -- V.2 Finite dimensional operator pencils -- V.3 Similarity of operators modulo a subspace -- V.4 Duality -- V.5 The eigenvalue completion problem and related problems -- V.6 A matrix equation -- Notes -- VI. Principal blocks -- VI.1 Structure theorem for principal blocks -- VI.2 The eigenvalue completion problem for principal blocks -- VI.3 The eigenvalue restriction problem for principal blocks -- Notes -- VII. General blocks -- VII.1 Block similarity invariants, completion and restriction problems -- VII.2 Structure theorems and canonical form -- VII.3 Proof of Proposition 2.2 -- VII.4 Proof of Theorems 1.1 and 2.1 -- VII.5 Finite dimensional operator pencils -- VII.6 Non-everywhere defined operators modulo a subspace -- VII.7 Duality of operator blocks -- VII.8 The eigenvalue completion problem -- Notes -- VIII. Off-diagonal blocks -- VIII.1 Structure theorems for off-diagonal blocks -- VIII.2 The eigenvalue completion and restriction problems -- Notes -- IX. Connections with linear systems -- IX.1 Linear input/output systems and transfer functions -- IX.2 Blocks and controllability -- IX.3 Blocks and observability -- IX.4 Minimal systems -- IX.5 Feedback and block similarity -- IX.6 Eigenvalue assignment and eigenvalue completion -- IX.7 Assignment of controllability indices and eigenvalue restriction -- IX.8 (A, B)-invariant subspaces -- IX.9 Output stabilization by state feedback -- IX.10 Output injection -- Notes -- X. Applications to matrix polynomials -- X.1 Preliminaries -- X.2 Matrix polynomials with prescribed zero structure -- X.3 Wiener-Hopf factorization and indices -- Notes -- XI. Applications to rational matrix functions -- XI.1 Preliminaries on pole pairs and null pairs -- XI.2 The one sided homogeneous interpolation problem -- XI.3 Homogeneous two sided interpolation -- XI.4 An auxiliary result on block similarity -- XI.5 Factorization indices for rational matrix functions -- Notes -- XII. Infinite dimensional operator blocks -- XII.1 Preliminaries -- XII.2 Main theorems about (P, I)-blocks -- XII.3 Main theorems for (I, Q)-blocks -- XII.4 Operator blocks on a separable Hilbert space -- XII.5 Spectral completion and assignment problems -- Notes -- XIII. Factorization of operator polynomials -- XIII.1 Preliminaries on null pairs and spectral triples -- XIII.2 Wiener-Hopf equivalence -- XIII.3 Wiener-Hopf factorization -- XIII.4 Wiener-Hopf factorization and strict equivalence -- XIII.5 The Fredholm case -- Notes -- XIV. Factorization of analytic operator functions -- XIV.1 Preliminaries on spectral triples -- XIV.2 Wiener-Hopf equivalence -- XIV.3 Wiener-Hopf factorization -- Notes -- XV. Eigenvalue completion problems for triangular matrices -- XV.1 U-similar and decomposed U-specified matrices -- XV.2 Invariants for U-similarity -- XV.3 Invariants and U-canonical form in the generic case -- XV.4 The diagonal of U-similar matrices -- XV.5 An eigenvalue completion problem -- XV.6 Applications -- Notes -- Append -- A.1 Root functions of regular analytic matrix functions -- A.2 Right Jordan pairs of regular analytic matrix functions -- A.3 Left Jordan pairs -- A.4 Jordan pairs and Laurent principal parts -- A.5 Global spectral data for regular analytic matrix functions -- Notes -- List of notations