I am having problem to proove that the group of circulant Matrices of size nxn, $C_n$ is isomorphic to $\frac{\mathbb{C}[x]}{<x^n-1>}$
2026-03-25 03:22:54.1774408974
Circulant Matrices and Ring of Polinomials
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Let $A$ be the circulant matrix with top row $ \pmatrix{0&1&0&\cdots&0}$. Then each circulant matrix is a polynomial in $A$. Moreover $A$ has minimum polynomial $X^n-1$.