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An iteration method for the symmetric solutions and the optimal approximation solution of the matrix equation AXB=C
An iteration method is constructed to solve the linear matrix equation AXB=C over symmetric X. By this iteration method, the solvability of the equation AXB=C over symmetric X can be determinedExpand
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The reflexive and anti-reflexive solutions of the matrix equation AX = B
Abstract An n × n complex matrix P is said to be a generalized reflection matrix if P H = P and P 2 = I . An n × n complex matrix A is said to be a reflexive (or anti-reflexive) matrix with respectExpand
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Two inverse eigenvalue problems for a special kind of matrices
In this paper, a special kind of matrices which are symmetric, all elements are equal to zero except for the first row, the first column and the diagonal elements, and the elements of the first rowExpand
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An iterative method for symmetric solutions and optimal approximation solution of the system of matrix equations A1XB1 = C1, A2XB2 = C2
Abstract The symmetric solutions of the system of matrix equations A1XB1 = C1, A2XB2 = C2 are too difficult to be obtained by applying matrices decomposition. In this paper, an iterative method isExpand
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The skew-symmetric orthogonal solutions of the matrix equation AX=B☆
Abstract An n × n real matrix X is said to be a skew-symmetric orthogonal matrix if XT = −X and XTX = I. Using the special form of the C–S decomposition of an orthogonal matrix with skew-symmetric kExpand
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The bisymmetric solutions of the matrix equation A1X1B1+A2X2B2+⋯+AlXlBl=C and its optimal approximation☆
Abstract A matrix A = ( a ij ) ∈ R n × n is said to be bisymmetric matrix if a ij = a ji = a n + 1 - j , n + 1 - i for all 1 ⩽ i , j ⩽ n . In this paper, an iterative method is constructed to findExpand
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The generalized anti-reflexive solutions for a class of matrix equations (BX = C, XD = E)
In this paper, the generalized anti-reflexive solution for matrix equations (BX = C, XD = E), which arise in left and right inverse eigenpairs problem, is considered. With the special properties ofExpand
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THE NEAREST BISYMMETRIC SOLUTIONS OF LINEAR MATRIX EQUATIONS ∗1)
The necessary and sufficient conditions for the existence of and the expressions for the bisymmetric solutions of the matrix equations (I) A1X1B1 +A2X2B2 +···+AkXkBk = D, (II) A1XB1 + A2XB2 + ···+Expand
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On the construction of a Jacobi matrix from its mixed-type eigenpairs
In this paper, an inverse eigenvalue problem of constructing a Jacobi matrix from its mixedtype eigenpairs is considered. The necessary and sufficient conditions for the existence and uniqueness ofExpand
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New symmetry preserving method for optimal correction of damping and stiffness matrices using measured modes
Measured and analytical data are unlikely to be equal due to measured noise, model inadequacies, structural damage, etc. It is necessary to update the physical parameters of analytical models forExpand
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