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Solving systems of nonlinear matrix equations involving Lipshitzian map**s
In this study, both theoretical results and numerical methods are derived for solving different classes of systems of nonlinear matrix equations...
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Biquaternions and their complex matrix representations
Some universal similarity equalities for biquaternions and their complex matrix representations are established. As applications, various results on...
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The maximal and minimal ranks of matrix expression with applications
We give in this article the maximal and minimal ranks of the matrix expression A-B 1 V 1 C 1 - B 2 V 2 C 2 - B 3 V 3 C 3 - B 4 V 4 C 4 with respect to V 1 , V 2 , V 3 , and V 4 . As...
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An analytical proof of Ogawa’s determinantal theorem
In this note, we propose a short proof, essentially based on differential calculus, of the Ogawa’s determinantal theorem, which itself is an...
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On Theorems of Halmos and Roth
This paper was motivated by a result of Halmos [1971] on the characterization of invariant subspaces of finite-dimensional, complex linear operators....
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The Discrete Algebraic Riccati Equation and Hermitian Block Toeplitz Matrices
This paper discusses the representation of the full set of solutions of the discrete algebraic Riccati equation in terms of two solutions, the...
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Positive fixed points for a class of nonlinear operators and applications
In this paper, we study the existence and uniqueness of positive solutions for a class of nonlinear operator equations on ordered Banach spaces....
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Complete study on a bi-center problem for the Z 2-equivariant cubic vector fields
For the planar Z 2 -equivariant cubic systems having two elementary focuses, the characterization of a bi-center problem and shortened expressions of...
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Absolute Continuity, Interpolation and the Lyapunov Order
We extend our Nevanlinna–Pick theorem for Hardy algebras and their representations to cover interpolation at the absolutely continuous points of the...
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Determinantal representations of the generalized inverses \(A_{T,S}^{(2)}\) over the quaternion skew field with applications
We first present some determinantal representations of one {1,5}-inverse of a quaternion matrix within the framework of a theory of the row and...
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Some Not-quite-elementary Operators
Necessary and sufficient conditions are given that an operator equation of the form...
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Inertias and ranks of some Hermitian matrix functions with applications
Let S be a given set consisting of some Hermitian matrices with the same size. We say that a matrix A ∈ S is maximal if A − W is positive...
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Stability of Invariant Subspaces of Quaternion Matrices
A quaternion invariant subspace of a quaternion matrix is said to be stable (in the sense of robustness) if every nearby matrix has an invariant...
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Accurate solutions of M-matrix algebraic Riccati equations
This paper is concerned with the relative perturbation theory and its entrywise relatively accurate numerical solutions of an M -matrix Algebraic...
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Ranks of the common solution to six quaternion matrix equations
A new expression is established for the common solution to six classical linear quaternion matrix equations A 1 X = C 1 , XB 1 = C ...
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Accurate solutions of M-matrix Sylvester equations
This paper is concerned with a relative perturbation theory and its entrywise relatively accurate numerical solutions of an M -matrix Sylvester...
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On the numerical solution of large-scale sparse discrete-time Riccati equations
We discuss the numerical solution of large-scale discrete-time algebraic Riccati equations (DAREs) as they arise, e.g., in fully discretized...
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Retracing the residual curve of a Lyapunov equation solver
Let A ∈ℝ n × n and let B ∈ℝ n × p and consider the Lyapunov matrix equation AX + XA T + BB T =0. If A + A T <0, then the extended Krylov subspace method (EKSM)...
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On Additive Decomposition of the Hermitian Solution of the Matrix Equation AXA* = B
The decomposition of a Hermitian solution of the linear matrix equation AXA * = B into the sum of Hermitian solutions of other two linear matrix...