Some results on matrix symmetries and a pattern recognition application
Some results on matrix symmetries and a pattern recognition application
复制标题
DOI：
10.1109/tassp.1986.1164890
复制
发表时间：
1986-08
期刊：
影响因子：
--
通讯作者：
L. Datta;S. Morgera
中科院分区：
文献类型：
--
作者：
L. Datta;S. Morgera
这种对应关系涉及在实践中经常遇到的各种矩阵对称性。证明了这类双对称矩阵在乘法下是不闭的，而中心对称矩阵在加法下形成一个Abel群，在乘法下形成一个非Abel群。对于中心厄米特矩阵的特殊情况，给出了类似于中心对称矩阵的结果。一个模式识别特征选择问题的简要讨论，包括演示的方式，这些结果可用于在实践中开发计算效率的算法。
This correspondence deals with various matrix symmetries frequently encountered in practice. It is shown that the class of doubly symmetric matrices is not closed under multiplication, whereas centrosymmetric matrices form an Abelian group under addition and a non-Abelian group under multiplication. Results similar to centrosymmetric matrices are presented for the special case of centro-Hermitian matrices. A brief discussion of a pattern recognition feature selection problem is included to demonstrate the manner in which these results may be utilized in practice for developing computationally efficient algorithms.