四元数向量和矩阵的秩

在四元数和四元数向量、矩阵空间上引入三种不同的实表示法则，将四元数列向量的左右线性相关性问题转换成实数域上向量的线性相关问题，由此获得用实矩阵的秩代替四元数矩阵列左秩和列右秩计算方法，同时得出四元数矩阵可逆的一些充要条件和一些新的四元数行列式定义．

The Rank of Quaternion Vector and Matrix

Three real transformations of quaternion vector and matrix were introduced. By using these transformations, the operation of quaternion vector and matrix will reduce to the operation of real vector and matrix. The right and left linear correlation of quaternion vectors will be replaced by the linear correlation of real vectors, the right and left column rank of quaternion matrix will be instead by the rank of real matrix. Some properties of invertible quaternion matrix were discussed and a new definition of quaternion was introduced in this paper.