The solution of the equationAX + BX⋆ = 0

DOI10.1080/03081087.2012.750656zbMath1292.15011OpenAlexW2061213330MaRDI QIDQ2872527

Fernando De Terán

Publication date: 15 January 2014

Published in: Linear and Multilinear Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/03081087.2012.750656

zbMATH Keywords

matrix equationsSylvester equationmatrix pencilsKronecker canonical formtransposeconjugate transpose

Mathematics Subject Classification ID

Matrix equations and identities (15A24) Canonical forms, reductions, classification (15A21) Matrix pencils (15A22) Toeplitz, Cauchy, and related matrices (15B05)

Related Items (6)

The solutions of the quaternion matrix equation \(AX^\varepsilon + BX^\delta = 0\) ⋮ Uniqueness of solution of a generalized \(\star\)-Sylvester matrix equation ⋮ The complete equivalence canonical form of four matrices over an arbitrary division ring ⋮ Root polynomials and their role in the theory of matrix polynomials ⋮ Coupled Sylvester-type Matrix Equations and Block Diagonalization ⋮ The solution of the equationAX + BX^⋆ = 0

Cites Work

• Iterative algorithms for the minimum-norm solution and the least-squares solution of the linear matrix equations \(A_1XB_1 + C_1X^TD_1 = M_1, A_2XB_2 + C_2 X^TD_2 = M_2\)
• On the \(\star\)-Sylvester equation \(AX\pm X^{\star} B^{\star} = C\)
• Gradient based and least squares based iterative algorithms for matrix equations \(AXB + CX^{T}D = F\)
• The solution of the equation \(XA+AX^T=0\) and its application to the theory of orbits
• An efficient algorithm for solving extended Sylvester-conjugate transpose matrix equations
• Iterative solutions to coupled Sylvester-transpose matrix equations
• Some matrix equations over a finite field
• Iterative algorithms for solving the matrix equation \(AXB + CX^{T}D = E\)
• Vibration of fast trains, palindromic eigenvalue problems and structure-preserving doubling algorithms
• Implicit QR algorithms for palindromic and even eigenvalue problems
• On the symmetric solutions of a linear matrix equation
• Roth's theorems for matrix equations with symmetry constraints
• The solution to matrix equation \(AX+X^TC=B\)
• The solution of the equationAX + BX^⋆ = 0
• The generalized centro-symmetric and least squares generalized centro-symmetric solutions of the matrix equation AYB + CYTD = E
• Structured Condition Numbers for Invariant Subspaces

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