【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.更多还原

【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.更多还原