Comparing a Matrix to its Off-Diagonal Part
Comparing a Matrix to its Off-Diagonal Part
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DOI：
10.1007/978-3-0348-9144-8_4
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发表时间：
1989
期刊：
影响因子：
--
通讯作者：
R. Bhatia;Man-Duen Choi;Chandler Davis
中科院分区：
文献类型：
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作者：
R. Bhatia;Man-Duen Choi;Chandler Davis
设对任意n×n复数矩阵，用零替换其所有对角线项的运算。对于各种矩阵范数，我们研究了MaxA|OA|/|A|。得到了上下界，但它们只对p=1，2，∞的范数成立。对于后一种范数，最大值的值也可以通过限制到子集A≥0来获得。
LetObe the operation which for anyn×ncomplex matrix replaces all its diagonal entries by zeroes. For various matrix norms, we study maxA|||OA|||/|||A|||. Upper and lower bounds are obtained, but they agree only for thecpnorms withp= 1, 2, ∞. For these latter norms, the value of the maximum is also obtained withArestricted to the subsetA≥ 0.