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Note on the weighted generalized inverse of the product of matrices
The weighted generalized inverse has several important applications in the theoretical research and numerical computations. In this paper, we present...
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Transforming algebraic Riccati equations into unilateral quadratic matrix equations
The problem of reducing an algebraic Riccati equation XCX − AX − XD + B = 0 to a unilateral quadratic matrix equation (UQME) of the kind PX ...
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The Non–symmetric Discrete Algebraic Riccati Equation and Canonical Factorization of Rational Matrix Functions on the Unit Circle
Canonical factorization of a rational matrix function on the unit circle is described explicitly in terms of a stabilizing solution of a discrete...
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On additive decompositions of solutions of the matrix equation AXB=C
This paper considers decompositions of solutions of the linear matrix equation AXB = C into the sums of solutions of other two linear matrix equations A ...
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Perturbation estimates for the nonlinear matrix equation X−A * X q A=Q (0<q<1)
The nonlinear matrix equation X − A * X q A = Q with 0< q <1 is investigated. Two perturbation estimates for the unique positive definite solution of the...
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The least squares problem of the matrix equation A 1 X 1 B
1 T + A 2 X 2 B2 T = TThe matrix least squares (LS) problem min X | AXB T − T | F is trivial and its solution can be simply formulated in terms of the generalized inverse of A ...
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Bezoutians Applied to Least Squares Approximation of Rational Functions
A projection method to reduce large scale discrete systems which has been introduced in au][12, 21] will be generalized to continues systems without...
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Meromorphic iterative roots of linear fractional functions
Iterative root problem can be regarded as a weak version of the problem of embedding a homeomorphism into a flow. There are many results on iterative...
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Extremal ranks of submatrices in an Hermitian solution to the matrix equation AXA *=B with applications
Suppose that AXA * = B is a consistent matrix equation and partition its Hermitian solution X * = X into a 2-by-2 block form. In this paper, we give some...
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A probabilistic interpretation of cyclic reduction and its relationships with logarithmic reduction
We provide a simple convergence proof for the cyclic reduction algorithm for M/G /1 type Markov chains together with a probabilistic interpretation...
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On the Hermitian positive defnite solution of the nonlinear matrix equation X + A*X −1 A + B*X −1 B = I
In this paper, we study the matrix equation X + A * X −1 A + B * X −1 B = I , where A, B are square matrices, and obtain some conditions for the existence...
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About the uniqueness solution of the matrix polynomial equation A(
λ )X(λ ) − Y(λ )B(λ ) = C(λ )We establish conditions for the existence of a unique solution of the matrix polynomial equation A ( λ ) X ( λ ) − Y ( λ ) B ( λ ) = C ( λ ) over an arbitrary field.
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The solvability conditions for inverse problems of anti-symmetric ortho-symmetric matrices
This paper discusses the anti-symmetric ortho-symmetric solution of a linear matrix equation and its optimal approximation. The necessary and...
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The anti-symmetric ortho-symmetric solution of a linear matrix equation and its optimal approximation
This paper discusses the anti-symmetric ortho-symmetric solution of a linear matrix equation and its optimal approximation. By the generalized...
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Matrix-Differential-Operator Approach to the Maxwell Equations and the Dirac Equation
We use matrix-differential-operators and Fourier expansion to solve the Maxwell equations and the free Dirac equation for any given initial...
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Matrix equation AXB = E with PX = sXP constraint
The matrix equation AXB = E with the constraint PX = sXP is considered, where P is a given Hermitian matrix satisfying P 2 = I and s = ±1. By an...
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The Noncommutative Bispectral Problem for Operators of Order One
We study a noncommutative version of the bispectral problem and consider the corresponding ad-conditions in the case when both operators have order...
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Least-Squares Solution with the Minimum-Norm for the Matrix Equation A T XB+B T X T A = D and Its Applications
An efficient method based on the projection theorem, the generalized singular value decomposition and the canonical correlation decomposition is...