对最佳鉴别矢量的求解方法进行了研究，根据矩阵的分块理论和优化理论，在一定的条件下，从理论上得到类间散布矩阵和总体散布矩阵的一种简洁表示方法，提出了求解最佳鉴别矢量的一种新算法，该算法的优点是计算量明显减少。ORL人脸数据库的数值实验，验证了上述论断的正确性。实验结果表明，虽然识别率与分块维数之间存在非线性关系，但可以通过选择适当的分块维数来获得较高的识别率。类间散布矩阵和总体散布矩阵的一种简洁表示方法适合于一切使用Fisher鉴别准则的模式识别问题。

A study has been made on the algorithm of solving optimal set of discriminant vectors in this paper. A concise representation method of between-class scatter matrix and population scatter matrix is proposed theoretically based on theories of blocking matrix and optimization under certain conditions. A new algebraic method of feature extraction is presented. The most obvious advantage of the proposed algorithm is that the computation time decreases drastically. The statement is supported by the numerical simulation experiments on facial database of ORL. The experimental results indicate that high recognition rate can be obtained through the appropriate selection of the dimension of block matrix although there exists nonlinear relationship between recognition rate and dimension of block matrix. The proposed concise representation method of scatter matrix suits for all the applications of pattern recognition using Fisher criteria.