منابع مشابه
On the Matrix Equation Xa − Ax = X
We study the matrix equation XA − AX = X p in M n (K) for 1 < p < n. It is shown that every matrix solution X is nilpotent and that the generalized eigenspaces of A are X-invariant. For A being a full Jordan block we describe how to compute all matrix solutions. Combinatorial formulas for A m X ℓ , X ℓ A m and (AX) ℓ are given. The case p = 2 is a special case of the algebraic Riccati equation.
متن کاملEla the Symmetric Minimal Rank Solution of the Matrix Equation Ax = B and the Optimal Approximation∗
By applying the matrix rank method, the set of symmetric matrix solutions with prescribed rank to the matrix equation AX = B is found. An expression is provided for the optimal approximation to the set of the minimal rank solutions.
متن کاملArnoldi and Jacobi-Davidson methods for generalized eigenvalue problems Ax=λBx with singular B
In many physical situations, a few specific eigenvalues of a large sparse generalized eigenvalue problem Ax = λBx are needed. If exact linear solves with A−σB are available, implicitly restarted Arnoldi with purification is a common approach for problems where B is positive semidefinite. In this paper, a new approach based on implicitly restarted Arnoldi will be presented that avoids most of th...
متن کاملOn the ⋆-Sylvester equation AX ± X⋆ B⋆ = C
We consider the solution of the ?-Sylvester equation AX±X?B? = C, for ? = T,H and A,B,∈ Cm×n, and some related linear matrix equations (AXB? ± X? = C, AXB? ± CX?D? = E, AX ± X?A? = C, AX ± Y B = C, AXB ± CY D = E, AXA? ± BY B? = C and AXB ± (AXB)? = C). Solvability conditions and stable numerical methods are considered, in terms of the (generalized and periodic) Schur, QR and (generalized) sing...
متن کاملA New Solution to the Matrix Equation X−AX¯B=C
We investigate the matrix equation X - AXB = C. For convenience, the matrix equation X - AXB = C is named as Kalman-Yakubovich-conjugate matrix equation. The explicit solution is constructed when the above matrix equation has unique solution. And this solution is stated as a polynomial of coefficient matrices of the matrix equation. Moreover, the explicit solution is also expressed by the symme...
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ژورنال
عنوان ژورنال: Journal of Mathematical Analysis and Applications
سال: 1967
ISSN: 0022-247X
DOI: 10.1016/0022-247x(67)90169-2