向量交换矩阵一种新的定义及应用

摘要

By using the Kronecker product of the identity matrix and the fundamental vector, a new definition of vec-permutation matrix is presented, which is simpler than the original one. Based on the new definition, the properties of the vec-permutation matrix are discussed. The proof of the equivalence between the new definition and the original one is given. At last, a new result on the singular values of Kroneker products of several matrices is established.%　　利用单位矩阵和基本向量给出了向量交换矩阵的一种较以往表述简单的新的定义。基于新的定义证明了向量交换矩阵的性质。给出了新定义与原有定义的等价性的证明。最后给出了矩阵克罗内克积奇异值的一个新的结论。