منابع مشابه
On the solving of matrix equation of Sylvester type
A solution of two problems related to the matrix equation of Sylvester type is given. In the first problem, the procedures for linear matrix inequalities are used to construct the solution of this equation. In the second problem, when a matrix is given which is not a solution of this equation, it is required to find such solution of the original equation, which most accurately approximates the ...
متن کاملOn the matrix equation
Article history: Received 8 July 2012 Accepted 22 October 2012 Available online 20 December 2012 Submitted by Froilan Dopico AMS classification: 15A24 15A21
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The matrix equation XA+ AXT = 0, which has relevance to the study of Lie algebras, was recently studied by De Terán and Dopico (Linear Algebra Appl. 434 (2011), 44–67). They reduced the study of this equation to several special cases and produced explicit solutions in most instances. In this note we obtain an explicit solution in one of the difficult cases, for which only the dimension of the s...
متن کاملOn 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 کاملSinc operational matrix method for solving the Bagley-Torvik equation
The aim of this paper is to present a new numerical method for solving the Bagley-Torvik equation. This equation has an important role in fractional calculus. The fractional derivatives are described based on the Caputo sense. Some properties of the sinc functions required for our subsequent development are given and are utilized to reduce the computation of solution of the Bagley-Torvik equati...
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series A
سال: 1980
ISSN: 0097-3165
DOI: 10.1016/0097-3165(80)90002-3