• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.7 no.2
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• pp.51-64
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• 2003

Analysis is given of construction and stability of complex symmetric analogues of Householder matrices, with applications to the eigenproblem for such matrices. We investigate numerical properties of the deflation of complex symmetric matrices by using complex symmetric Householder transformations. The proposed method is very similar to the well-known deflation technique for real symmetric matrices (Cf. [16], pp. 586-595). In this paper we present an error analysis of one step of the deflation of complex symmetric matrices.

• Bulletin of the Korean Mathematical Society
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• v.52 no.4
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• pp.1269-1283
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• 2015

An operator $T{{\in}}{\mathcal{L}}({\mathcal{H}})$ is said to be skew complex symmetric if there exists a conjugation C on ${\mathcal{H}}$ such that $T=-CT^*C$. In this paper, we study properties of skew complex symmetric operators including spectral connections, Fredholmness, and subspace-hypercyclicity between skew complex symmetric operators and their adjoints. Moreover, we consider Weyl type theorems and Browder type theorems for skew complex symmetric operators.

• Kyungpook Mathematical Journal
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• v.63 no.2
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• pp.287-311
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• 2023

In this paper, we introduce the notion of cyclic structure Jacobi semi-symmetric real hypersurfaces in the complex hyperbolic quadric Q^m* = SO⁰_2,m/SO₂SO_m. We give a classifiction of when real hypersurfaces in the complex hyperbolic quadric Q^m* having 𝔄-principal or 𝔄-isotropic unit normal vector fields have cyclic structure Jacobi semi-symmetric tensor.

• Journal of the Korean Mathematical Society
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• v.52 no.6
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• pp.1271-1286
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• 2015

An operator T on a complex Hilbert space H is called skew symmetric if T can be represented as a skew symmetric matrix relative to some orthonormal basis for H. In this paper, we study skew symmetric operators with eigenvalues. First, we provide an upper-triangular operator matrix representation for skew symmetric operators with nonzero eigenvalues. On the other hand, we give a description of certain skew symmetric triangular operators, which is based on the geometric relationship between eigenvectors.

• Journal of the Korean Mathematical Society
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• v.52 no.2
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• pp.403-416
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• 2015

An operator T on a complex Hilbert space $\mathcal{H}$ is called skew symmetric if T can be represented as a skew symmetric matrix relative to some orthonormal basis for $\mathcal{H}$. In this note, we explore the structure of skew symmetric operators with disconnected spectra. Using the classical Riesz decomposition theorem, we give a decomposition of certain skew symmetric operators with disconnected spectra. Several corollaries and illustrating examples are provided.

• Journal of the Korean Mathematical Society
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• v.58 no.4
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• pp.799-817
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• 2021

In this paper, we investigate the normal and complex symmetric weighted composition operators W_𝜓,𝜑 on the Hardy space H²(𝔻). Firstly, we give the explicit conditions of weighted composition operators to be normal and complex symmetric with respect to conjugations 𝒞₁ and 𝒞₂ on H²(𝔻), respectively. Moreover, we particularly investigate the weighted composition operators W_𝜓,𝜑 on H²(𝔻) which are normal and complex symmetric with respect to conjugations 𝓙, 𝒞₁ and 𝒞₂, respectively, when 𝜑 has an interior fixed point, 𝜑 is of hyperbolic type or parabolic type.

• Bulletin of the Korean Mathematical Society
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• v.60 no.4
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• pp.849-861
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• 2023

In this paper, we introduce the notion of semi-symmetric structure Jacobi operator for Hopf real hypersufaces in the complex quadric Q^m = SO_m+2/SO_mSO₂. Next we prove that there does not exist any Hopf real hypersurface in the complex quadric Q^m = SO_m+2/SO_mSO₂ with semi-symmetric structure Jacobi operator. As a corollary, we also get a non-existence property of Hopf real hypersurfaces in the complex quadric Q^m with either symmetric (parallel), or recurrent structure Jacobi operator.

• Journal of applied mathematics & informatics
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• v.9 no.2
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• pp.891-897
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• 2002

A symmetric minimal complement at infinity for a given symmetric Silvester data set in the complex plane is contructed.

• Bulletin of the Korean Mathematical Society
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• v.60 no.5
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• pp.1141-1154
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• 2023

In this paper, we study the complex symmetric weighted composition-differentiation operator D_𝜓,𝜙 with respect to the conjugation JW_𝜉,𝜏 on the Hardy space H². As an application, we characterize the necessary and sufficient conditions for such an operator to be normal under some mild conditions. Finally, the spectrum of D_𝜓,𝜙 is also investigated.

• Bulletin of the Korean Mathematical Society
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• v.60 no.5
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• pp.1181-1199
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• 2023

For solving complex symmetric positive definite linear systems, we propose a single step real-valued (SSR) iterative method, which does not involve the complex arithmetic. The upper bound on the spectral radius of the iteration matrix of the SSR method is given and its convergence properties are analyzed. In addition, the quasi-optimal parameter which minimizes the upper bound for the spectral radius of the proposed method is computed. Finally, numerical experiments are given to demonstrate the effectiveness and robustness of the propose methods.