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1·State matrix is diagonalized according to the orthonormality of left and right eigenvector series about the state matrix.

最后根据状态矩阵的左右特征向量系的正交性，对给出的状态矩阵进行对角化。

2·This paper presents a direct solution to the left eigenvector of the asymmetrical matrix under the condition that the eigenvalue and the right eigenvector are known.

本文在特征值及右特征向量均为已知的条件下，提出一种直接求解左特征向量的方法。

3·The MSVD method constructs a self-contained orthogonal basis using the outer product of left and right eigenvector matrixes decomposed from 2D geochemical or geophysical maps.

该方法首先对地球物理和地球化学等网格数据进行二维矩阵的奇异值分解，之后用左特征向量矩阵与右特征向量矩阵的直积构造一个正交完备基。

4·We proved that each square quaternion matrix has at least one right characteristic principal value and its eigenvector, and a concrete solution was given.

证明了对每一个四元数矩阵，至少存在一个右特征主值，存在一个属于它的特征向量，并给出了具体的求解方法。

5·The results showed why the right principal eigenvector of a judgement matrix can be regarded as the priority vector. Consistency test to a judgement matrix is also discussed.

指出了用判断矩阵的右特征向量作为排序向量的理由，并且还讨论了判断矩阵的一致性检验问题。