A lower bound for the product of eigenvalues of solutions to matrix equations
نویسندگان
چکیده
The following matrix equations: ATXB+ BTXTA = C and ATXB+ BTXA = C, are encountered in many systems and control applications, and these matrix equations contain several linear matrix equations as special cases. In the present work, we introduce the inequalities for the determinant of the solutions of these matrix equations, separately. Then using these inequalities, we introduce a lower bound for the product of eigenvalues of the solutions to the matrix equations. © 2009 Elsevier Ltd. All rights reserved.
منابع مشابه
Separable programming problems with the max-product fuzzy relation equation constraints
In this paper, the separable programming problem subject to Fuzzy Relation Equation (FRE) constraints is studied. It is decomposed to two subproblems with decreasing and increasing objective functions with the same constraints. They are solved by the maximum solution and one of minimal solutions of its feasible domain, respectively. Their combination produces the original optimal solution. The ...
متن کاملPosynomial geometric programming problem subject to max–product fuzzy relation equations
In this article, we study a class of posynomial geometric programming problem (PGPF), with the purpose of minimizing a posynomial subject to fuzzy relational equations with max–product composition. With the help of auxiliary variables, it is converted convert the PGPF into an equivalent programming problem whose objective function is a non-decreasing function with an auxiliary variable. Some pr...
متن کاملA spectral method based on Hahn polynomials for solving weakly singular fractional order integro-differential equations
In this paper, we consider the discrete Hahn polynomials and investigate their application for numerical solutions of the fractional order integro-differential equations with weakly singular kernel .This paper presented the operational matrix of the fractional integration of Hahn polynomials for the first time. The main advantage of approximating a continuous function by Hahn polynomials is tha...
متن کاملThe (R,S)-symmetric and (R,S)-skew symmetric solutions of the pair of matrix equations A1XB1 = C1 and A2XB2 = C2
Let $Rin textbf{C}^{mtimes m}$ and $Sin textbf{C}^{ntimes n}$ be nontrivial involution matrices; i.e., $R=R^{-1}neq pm~I$ and $S=S^{-1}neq pm~I$. An $mtimes n$ complex matrix $A$ is said to be an $(R, S)$-symmetric ($(R, S)$-skew symmetric) matrix if $RAS =A$ ($ RAS =-A$). The $(R, S)$-symmetric and $(R, S)$-skew symmetric matrices have a number of special properties and widely used in eng...
متن کاملThe Structure of Bhattacharyya Matrix in Natural Exponential Family and Its Role in Approximating the Variance of a Statistics
In most situations the best estimator of a function of the parameter exists, but sometimes it has a complex form and we cannot compute its variance explicitly. Therefore, a lower bound for the variance of an estimator is one of the fundamentals in the estimation theory, because it gives us an idea about the accuracy of an estimator. It is well-known in statistical inference that the Cram&eac...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- Appl. Math. Lett.
دوره 22 شماره
صفحات -
تاریخ انتشار 2009