反循环矩阵及广义反循环矩阵的若干性质

Some Properties of the Anti-Circular Matrix and Generalized Anti-Circular Matrix

可表示为非奇异对角矩阵和反循环矩阵乘积的矩阵,我们称其为广义反循环矩阵。本文给出了单位矩阵与反循环矩阵的和矩阵以及单位矩阵与广义反循环矩阵的和矩阵为非奇异的充要条件,得到了这样和矩阵的相对增益阵列的显示表达式。

We call a matrix the generalized anti - cyclic matrix if it can be written the product of a nonsingular diagonal matrix and a anti -cyclic matrix. This paper gives the sufficient and necessary conditions for the sum of a identity matrix and a anti - cyclic matrix, the sum of a identity matrix and a generalized anti - cyclic matrix is nonsingular, and obtain the formal representation of the relative gain array of the sum matrix.