【摘要】 对于矩阵D₁和D₂是非负定时,本文给出行列式之比|X’AY|²/(|X’D₁X||Y’D₂Y|和矩阵之迹[tr（X’AY）]²在约束X’D₁X=I_k,Y’D₂Y=I_k的极值,这一结果把作者文[5]的极值结果推广到D₁,D₂可能奇异的情况。本文把所得到的极值结果应用到多元分析,说明文章[1]定义的几种广义相关系数的极值性质,从而分别给出几种广义相关系数一种统计解释。更多还原

【Abstract】 In this paper, we give extremes of the ratio of determinantsand the trace of matrix [tr(X’AY]2 under contrains X’ D1X = IK and Y’ D2Y = IK when D1 and D2 are non-negative definite. Results obtained are the generalizations of the results obtained by author[5] when DI and D2 are positive definite. These extremes are applied to multivariate analysis. The extreme properties of generlized Correlation Coefficients between two random vecters definitted by paper[1] are obtained, so that statistical meanings of generalized correlation coefficients are also explained.更多还原