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Tongxing Lu (1986)
Solution of the matrix equation AX-XB=CComputing, 37
Arlen Brown, C. Pearcy (1965)
Structure of Commutators of OperatorsAnnals of Mathematics, 82
Allen Schweinsberg (1982)
The operator equation $AX-XB=C$ with normal $A$ and $B$.Pacific Journal of Mathematics, 102
W. Roth (1952)
The equations $AX-YB=C$ and $AX-XB=C$ in matrices, 3
R. Hartwig (1972)
Resultants and the Solution of $AX - XB = - C$Siam Journal on Applied Mathematics, 23
G. Stewart (1973)
Error and Perturbation Bounds for Subspaces Associated with Certain Eigenvalue ProblemsSiam Review, 15
D. Herrero (1984)
Approximation of Hilbert Space Operators
P. Lancaster, M. Tismenetsky (1969)
The theory of matrices
(1973)
Inariant subspaces (Springer
N. Higham (1994)
The matrix sign decomposition and its relation to the polar decompositionLinear Algebra and its Applications
E. Souza, S. Bhattacharyya (1981)
Controllability, observability and the solution of AX - XB = CLinear Algebra and its Applications, 39
L. Fialkow (1979)
A note on norm ideals and the operatorX→AX−XBIsrael Journal of Mathematics, 32
(1984)
Numerical solution of certain algebraic problems arising in the theory of stability
L. Fialkow (1978)
A Note on the Operator X →AX - XBTransactions of the American Mathematical Society, 243
W. Parker (1950)
The matrix equation $AX=XB$Duke Mathematical Journal, 17
L. Dieci (1991)
Some numerical considerations and Newton's method revisited for solving algebraic Riccati equationsIEEE Transactions on Automatic Control, 36
(1993)
Perturbation theory and backward error for AXkXB l C
(1974)
Commutativity and separation of spectra II
G. Lumer, M. Rosenblum (1959)
Linear operator equations, 10
G. Golub, S. Nash, C. Loan (1979)
A Hessenberg-Schur method for the problem AX + XB= CIEEE Transactions on Automatic Control, 24
R. Bellman (1972)
Introduction to Matrix Analysis
J. Goldstein (1978)
On the operator equation $AX+XB=Q$, 70
R. Smith (1968)
Matrix Equation $XA + BX = C$Siam Journal on Applied Mathematics, 16
D. Hu, L. Reichel (1992)
Krylov-subspace methods for the Sylvester equationLinear Algebra and its Applications, 172
K. Datta (1988)
The matrix equation XA − BX = R and its applicationsLinear Algebra and its Applications, 109
(1967)
Stability of motion (Springer
R. Bhatia (1994)
First and second order perturbation bounds for the operator absolute valueLinear Algebra and its Applications
S. Sen, G. Howell (1992)
Direct fail-proof triangularization algorithms for AX + XB = C with Error-Free and parallel implementationsApplied Mathematics and Computation, 50
(1994)
Operator substitution
R. Hartwig (1975)
$AX - XB = C$, Resultants and Generalized InversesSiam Journal on Applied Mathematics, 28
L. Fialkow (1981)
Elements of Spectral Theory for Generalized Derivations II : The Semifredholm DomainCanadian Journal of Mathematics, 33
高维新 (1986)
The Continued Fraction Solution of the Matrix Equation AX-XB=C, 15
V. Phóng (1991)
The operator equationAX−XB=C with unbounded operatorsA andB and related abstract Cauchy problemsMathematische Zeitschrift, 208
(1964)
Some new studies of perturbation theory of self-adjoint operators
Chandler Davis, P. Rosenthal (1974)
Solving Linear Operator EquationsCanadian Journal of Mathematics, 26
C. Lu (1971)
Solution of the matrix equation AX+XB = CElectronics Letters, 7
F. Smithies (1968)
A HILBERT SPACE PROBLEM BOOKJournal of The London Mathematical Society-second Series
Joseph Salle, S. Lefschetz, R. Alverson (1962)
Stability by Liapunov's Direct Method With ApplicationsPhysics Today, 15
M. Embry, M. Rosenblum (1974)
Spectra, tensor products, and linear operator equations.Pacific Journal of Mathematics, 53
(1980)
Spectral consequences of the existence of intertwining operators
C. Akemann, Phillip Ostrand (1976)
The Spectrum of a Derivation of a C*-AlgebraJournal of The London Mathematical Society-second Series
T. Mazumdar (1990)
Existence of solution of the operator equation AX − XB = Q with possibly unbounded A, B, QComputers & Mathematics With Applications, 19
R. Bhatia, Chandler Davis, P. Koosis (1989)
An extremal problem in Fourier analysis with applications to operator theoryJournal of Functional Analysis, 82
J. Varah (1979)
On the Separation of Two MatricesSIAM Journal on Numerical Analysis, 16
J. Williams (1969)
Similarity and the numerical rangeJournal of Mathematical Analysis and Applications, 26
(1953)
On the asymptotic solution of a vector differential equation
S. Shaw, S. Lin (1988)
On the equations Ax = q and SX − XT = QJournal of Functional Analysis, 77
(1992)
Distributed and shared memory block algorithms for the triangular Sylvester equation with Sep−" estimators
J. Hearon (1977)
Nonsingular solutions of TA−BT=CLinear Algebra and its Applications, 16
J. Barlow, M. Monahemi, D. O’Leary (1992)
Constrained Matrix Sylvester EquationsSIAM J. Matrix Anal. Appl., 13
H. Flanders, H. Wimmer (1977)
On the matrix equations $AX - XB = C$ and $AX - YB = C$Siam Journal on Applied Mathematics, 32
J. Maclagan-Wedderburn (1903)
Note on the Linear Matrix Equation, 22
W. Gao (1989)
CONTINUED-FRACTION SOLUTION OF MATRIX EQUATION AX-XB=C
(1987)
Perturbation bounds for matrix eigenalues (Longman
(1979)
Linear multiariable control—a geometric approach (Springer, Berlin
(1954)
Spectral operators
(1953)
U> ber die
Sur l'equation en matrices px l xq
W. Arendt, F. Räbiger, A. Sourour (1994)
SPECTRAL PROPERTIES OF THE OPERATOR EQUATION AX + XB = YQuarterly Journal of Mathematics, 45
L. Lerer, L. Rodman (1993)
Sylvester and Lyapunov equations and some interpolation problems for rational matrix functionsLinear Algebra and its Applications, 185
P. Enflo (1987)
On the invariant subspace problem for Banach spacesActa Mathematica, 158
P. Lancaster, L. Lerer, M. Tismenetsky (1984)
Factored forms for solutions of AX − XB = C and X − AXB = C in companion matricesLinear Algebra and its Applications, 62
P. Lancaster (1970)
Explicit Solutions of Linear Matrix EquationsSiam Review, 12
Chandler Davis, W. Kahan (1970)
The Rotation of Eigenvectors by a Perturbation. IIISIAM Journal on Numerical Analysis, 7
M. Rosenblum (1956)
On the operator equation $BX-XA=Q$Duke Mathematical Journal, 23
D. Powers (1976)
Solving AX + XB = C by control and tearingInternational Journal of Control, 23
G. Starke, W. Niethammer (1991)
SOR for AX−XB=CLinear Algebra and its Applications
John Jones (1974)
Explicit solutions of the matrix equationAX−XB=CRendiconti del Circolo Matematico di Palermo, 23
A. Ostrowski, H. Schneider (1962)
Some theorems on the inertia of general matricesJournal of Mathematical Analysis and Applications, 4
(1971)
Hyperinvariant subspaces for spectral and n-normal operators
J. Roberts (1980)
Linear model reduction and solution of the algebraic Riccati equation by use of the sign functionInternational Journal of Control, 32
R. Bellman (1997)
Introduction to matrix analysis (2nd ed.)
R. Bhatia (1994)
Matrix factorizations and their perturbationsLinear Algebra and its Applications
(1985)
Matrix analysis (Cambridge
(1947)
Problemes geT neT ral de la stabiliteT du mou ement (1892) ; reprinted as Ann
J. Kyle (1978)
Ranges of Lyapunov Transformations for operator algebrasGlasgow Mathematical Journal, 19
M. Rosenblum (1969)
The operator equation $BX-XA=Q$ with self-adjoint $A$ and $B$, 20
R. Byers (1984)
A LINPACK-style condition estimator for the equation AX-XB^{T} = CIEEE Transactions on Automatic Control, 29
H. Bercovici (1990)
Notes on invariant subspacesBulletin of the American Mathematical Society, 23
V. Lovass-Nagy, D. Powers (1976)
On Least Squares Solutions of an Inconsistent Singular Equation $AX + XB = C$Siam Journal on Applied Mathematics, 31
Er-Chieh Ma (1966)
A Finite Series Solution of the Matrix Equation $AX - XB = C$Siam Journal on Applied Mathematics, 14
P. Rosenthal (1982)
On the equations X=KXS and AX=XKBanach Center Publications, 8
Ren-Cang Li (1995)
New Perturbation Bounds for the Unitary Polar FactorSIAM J. Matrix Anal. Appl., 16
(1951)
Beitra$ ge zur Sto$ rungstheorie der Spektralzerlegung
Error bounds for the equation AXjXB l C ', Matrix Tensor Quart
R. Bhatia, Chandler Davis, A. Mcintosh (1983)
Perturbation of spectral subspaces and solution of linear operator equationsLinear Algebra and its Applications
The entities A, B, X, Y in the title are operators, by which we mean either linear transformations on a finite‐dimensional vector space (matrices) or bounded (= continuous) linear transformations on a Banach space. (All scalars will be complex numbers.) The definitions and statements below are valid in both the finite‐dimensional and the infinite‐dimensional cases, unless the contrary is stated. 1991 Mathematics Subject Classification 15A24, 47A10, 47A62, 47B47, 47B49, 65F15, 65F30.
Bulletin of the London Mathematical Society – Wiley
Published: Jan 1, 1997
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