广义多元统计中矩阵W_2^(-1)W_1的特征值、特征向量分布

The Distribution of Characteristic Values and Characteristic Vectors for Matrix W_2^(-1)W_1 in Generalized Multivariate Statistics

在X =X1X2～LSn×p(f)的条件下 ,推导了矩阵 (X′2 X2 ) -1(X′1X1)特征值的联合分布及相应的特征向量构成的随机矩阵的联合分布 ,从而可不通过矩阵Beta ,广义矩阵F的联合分布 ,直接得到它们特征值的联合分布 .

In the given condition the joint distribution of X=X_1 X_2～LS_(n×p)(f) characteristic values and their correspondent characteristic vectors for matrix (X′_2X_2)^(-1)(X′_1X_1) are derived, so the joint distribution of matrix Beta distribution and matrix distribution are derived directly and respectively, without using their joint distribution.