ON SKEW SYMMETRIC OPERATORS WITH EIGENVALUES
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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 op- erator matrix representation for skew symmetric operators with nonzero eigenvalues. On the other hand, we give a description of certain skew sym- metric triangular operators, which is based on the geometric relationship between eigenvectors.
Abstract
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 op- erator matrix representation for skew symmetric operators with nonzero eigenvalues. On the other hand, we give a description of certain skew sym- metric triangular operators, which is based on the geometric relationship between eigenvectors.
참고문헌 (20)
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