矩阵的Frobenius范数的极值

2011 Fourth International Joint Conference on Computational Sciences and Optimization Pub Date : 2011-04-15 DOI:10.1109/CSO.2011.267

Kaifan Yang

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摘要

对于两个给定的矩阵A和B，当X遍历酉矩阵时，矩阵B- xa的Frobenius范数的极值成立。利用奇异值分解技术，研究了Frobenius范数矩阵的极值问题。结果表明，当X遍历酉矩阵时，矩阵B-XA具有极值，并给出了Frobenius范数的最大值和最小值的有界。

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The Extremum of the Frobenius Norm of Matrix

For two given matrices A and B, the extremum of the Frobenius norm of matrix B-XA is established when X is running all over the unitary matrices. By using the technique of singular value decomposition, the extremum of the Frobenius norm matrix is studied. The result shows that the matrix B-XA has extremum when X is running all over the unitary matrices and in this paper, the bounded of maximum and the minimum of the Frobenius norm is obtained.

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2011 Fourth International Joint Conference on Computational Sciences and Optimization

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