ESTIMATE FOR DISTANCE-COEFFICIENT OF MATRICES |
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摘 要: | ESTIMATEFORDISTANCE┐COEFFICIENTOFMATRICESLUFANGYANAbstract.MotivationofthispaperisanopenproblemexposedbyB.Beauzamy[1].LetMbea...
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关 键 词: | 距离系数 矩阵 对角线代数 估计 |
收稿时间: | 4 June 1996 |
Estimate for distance-coefficient of matrices |
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Authors: | Lu Fangyan |
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Institution: | (1) Department of Mathematics, Zhejiang University, 310027 Hangzhou |
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Abstract: | Motivation of this paper is an open problem exposed by B. Beauzamy l]. Let M be a 3 X 3 matrix and d(M) is the distance to the diagonal algebra. Let α(M) = sup{∥P1
MP∥:P is a projection in the diagonal algebra} and then call K(M) = d(M)/α(M) the distance-coefficient of M. The following results are obtained: (1) If M’ has two zero-entries apart from its diagonal. then K(M) ≤3/2√2: (2) If M has one zero-entry apart from its diagonal, then K(M) ≤ √41/32; (3) If M is arbitrary, then K(M) √3/2.
This subject is supported by the National Natural Science Foundation of China and Natural Science Foundation of Zhejiang Province. |
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Keywords: | Matrix distance coefficient |
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