【摘要】 本文由有限域上交错矩阵方程ＸＫ２υＸ′＝０的解数公式得到ｑ超几何级数２Φ０的一个基本恒等式，并且用它能直接把一些特殊矩阵的这类方程的解数由函数２Φ０表出．另外还用２Φ０的一个恒等式得出Ｆｑ上ｍ阶特殊矩阵的个数．更多还原

【Abstract】 In this paper, an elementary identity for q hypergeometric series 2Φ 0 is obtained from two formulas of the number of solutions to the alternate equation XK 2υ X′=0 . Using this identity, formulas of the number of solutions of some special matrix equations are represented by q hypergeometric series. Finally, using another identity of 2Φ 0 , the numbers of some special matrices over F q are also obtained.更多还原