In training phase, singular value vector of a lot of face image information matrix from face image sets constitutes face image sets characteristic matrix as a column.

But it is very difficult to compute the number of non-negative matrix with fixed score row or column vectors, so to compute the number of tournament matrix with fixed score vector is also difficult.

This article analyzes a few profound concepts, such as companion matrix, line vector, column rector, orthogonal matrix, and recommend many qualities, which are difficult to grasp for many students.