奇特征有限域上非奇异对称矩阵方程解数公式  

THE NUMBER OF SOLUTIONS TO THE NONSINGULAR SYMMETRIC MATRIX EQUATION OVER A FINITE FIELD OF ODD CHARACTERISTIC

作　　者：魏鸿增[1] 张谊宾[1] 

机构地区：[1]河北师范大学

出　　处：《数学杂志》1998年第1期49-56,共8页Journal of Mathematics

基　　金：国家自然科学基金;河北省教委科研资助项目

摘　　要：设Ｆｇ是特征≠２的有限域，本文利用Ｆｇ上正交几何的理论，给出当Ａ是Ｆｇ上２υ＋ｒ阶非奇异对称矩阵时，Ｆｑ上适合方程ＸＡＸ′＝Ｂ的秩ｋ的解Ｘ的个数和解Ｘ的个数的明显公式。Let Fq be a finite field with q elements,where q is a power of an odd prime.In this paper,using orthogonal geometry over Fq,we have given the number of solutions X of rank k and the number of solutions X to theequation XAX′=B over Fq,where A is an nonsingular symmetric matric of order 2υ+δ.Finally,we haveobtained simple representation of enumerational formulas using qhypergeometric series.

关 键 词：对称矩阵方程 正交空间 Q超几何级数 

分 类 号：O151.21[理学—数学]