| 关于广义Hadamard矩阵及其对应有向图类的特征 |
| |
| 引用本文： | 卜长江,孙兵.关于广义Hadamard矩阵及其对应有向图类的特征[J].哈尔滨工程大学学报,2006,27(4):608-610. |
| |
| 作者姓名： | 卜长江 孙兵 |
| |
| 作者单位： | 哈尔滨工程大学,理学院,黑龙江,哈尔滨,150001;哈尔滨工程大学,自动化学院,黑龙江,哈尔滨,150001 |
| |
| 摘 要： | Hadamard矩阵在信号处理方面有重要应用,而Hadamard矩阵是广义Hadamard矩阵的特殊情形.讨论了广义Hadamard矩阵对应简单有向图类的特征及其相互关系;给出了广义Hadamard矩阵对应简单有向图的特征值的性质,从而证明了有向图的邻接矩阵是广义Hadamard矩阵的必要条件,为简单有向图是偶阶的;并得到了广义Hadamard矩阵在Kronecker积下的性质.为区组设计和编码理论提供了一些新的方法,并在信源编码中有重要的应用.
|
| 关 键 词： | 广义Hadamard矩阵 有向图 邻接矩阵 |
| 文章编号： | 1006-7043(2006)02-0608-03 |
| 修稿时间： | 2005年1月10日 |
Characteristics of generalized Hadamard matrices and corresponding digraphs |
| |
| BU Chang-jiang,SUN Bing.Characteristics of generalized Hadamard matrices and corresponding digraphs[J].Journal of Harbin Engineering University,2006,27(4):608-610. |
| |
| Authors: | BU Chang-jiang SUN Bing |
| |
| Abstract: | A significant amount of research has been done on Hadamard matrix applications and signal processing because of their binary characteristics and orthogonal properties.Here,the characteristics and eignenvalue properties of generalized Hadamard matrices and corresponding digraphs were presented.The property of Kronecker product for a generalized Hadamard matrix was also discussed.Furthermore,Hadamard matrix applications in block design and coding theory are extended,new methods for block design and coding theory are given,and the importance of its applications in source coding of signal processing is shown. |
| |
| Keywords: | generalized Hadamard matrix digraph adjacency matrix |
| 本文献已被 CNKI 维普 万方数据 等数据库收录！ |
|
