We consider two (densely defined) involutions on the space of $q\times q$matrices; $I(x_{ij})$ is the matrix inverse of $(x_{ij})$, and $J(x_{ij})$ isthe matrix whose $ij$th entry is the reciprocal $x_{ij}^{-1}$. Let $K=I\circJ$. The set ${\cal SC}_q$ of symmetric, cyclic matrices is invariant under $K$.In this paper, we determine the degrees of the iterates $K^n=K\circ...\circ K$restricted to ${\cal SC}_q$.
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机译：我们考虑在$ q \ times q $ matrices的空间上进行两次（密集定义）对合； $ I（x_ {ij}）$是$（x_ {ij}）$的矩阵逆，而$ J（x_ {ij}）$是其$ ij $ th项是倒数$ x_ {ij} ^的矩阵{-1} $。设$ K = I \ circJ $。对称循环矩阵的集合$ {\ cal SC} _q $在$ K $下不变。在本文中，我们确定迭代$ K ^ n = K \ circ ... \ circ K $的次数$ {\ cal SC} _q $。
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