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Inequalities of Hlawka type for matrices
被引：0
作者：
S. Wada
机构：
[1] Department of Information and Computer Engineering,
[2] Kisarazu National College of Technology,undefined
[3] 2-11-1 Kiyomidai-Higashi,undefined
[4] Kisarazu,undefined
[5] Chiba,undefined
[6] 292-0041 Japan,undefined
来源：
Archiv der Mathematik
|
2001年
/
77卷
关键词：
Complex Number;
Trace Norm;
Related Inequality;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
A generalized Hlawka's inequality says that for any n\documentclass[12pt]{minimal}
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$ (\geqq 2) $\end{document} complex numbers¶x1, x2, ..., xn,¶¶\documentclass[12pt]{minimal}
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$ \sum_{i=1}^n\Bigg|x_i - \sum_{j=1}^{n}x_j\Bigg| \leqq \sum_{i=1}^{n}|x_i| + (n - 2)\Bigg|\sum_{j=1}^{n}x_j\Bigg|. $\end{document}¶¶ We generalize this inequality to the trace norm and the trace of an n x n matrix A as¶¶\documentclass[12pt]{minimal}
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$ ||A - {\rm Tr} A ||_1\ \leqq ||A||_1 + (n - 2)| {\rm Tr} A|. $\end{document}¶¶ We consider also the related inequalities for p-norms \documentclass[12pt]{minimal}
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$ (1 \leqq p \leqq \infty) $\end{document} on matrices.
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页码：415 / 422
页数：7
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