| 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： | 1996-06-04 |
Estimate for distance-coefficient of matrices |
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| Lu Fangyan. Estimate for distance-coefficient of matrices[J]. Applied Mathematics A Journal of Chinese Universities, 1997, 12(4): 441-446. DOI: 10.1007/s11766-997-0046-3 |
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| Authors: | Lu Fangyan |
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| Affiliation: | (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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