The operator equation \(\sum _{i=0}^n A^{n-i}XB^i=Y\)

DOI10.1016/j.exmath.2009.02.001zbMath1167.15010OpenAlexW2746605060MaRDI QIDQ1028223

Rajendra Bhatia, Mitsuru Uchiyama

Publication date: 30 June 2009

Published in: Expositiones Mathematicae (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.exmath.2009.02.001

zbMATH Keywords

Fréchet derivativelinear operator equationSylvester equation

Mathematics Subject Classification ID

Matrix equations and identities (15A24) Equations and inequalities involving linear operators, with vector unknowns (47A50)

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Perturbation bounds for Mostow's decomposition and the bipolar decomposition ⋮ A Taylor expansion of the square root matrix function ⋮ Positive semidefinite solutions of the operator equation ⋮ H s -class construction of an almost invariant slow subspace for the Klein–Gordon equation in the non-relativistic limit ⋮ Resolvents of functions of operators with Hilbert-Schmidt hermitian components ⋮ Triangular representations of functions of operators with Schatten–von Neumann Hermitian components ⋮ Comprehensive survey on an order preserving operator inequality ⋮ Some properties of Furuta type inequalities and applications ⋮ Generalized product of two square matrices and application for some algebraic equations ⋮ Fréchet derivatives for operator monotone functions ⋮ Analytic functional calculus for two operators ⋮ Norm estimates for solutions of polynomial operator equations ⋮ ON THE SENSITIVITY OF THE SOLUTION OF THE GENERALIZED LYAPUNOV EQUATION

Cites Work

• Derivatives of the matrix exponential and their computation
• The Sensitivity of the Matrix Exponential
• How and Why to Solve the Operator Equation AX −XB = Y
• Means for matrices and comparison of their norms
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