Does there exist a matrix $\mathbf{A}$ that takes any vector $\mathbf{v}\in \mathbb{R}^n$ such that matrix $\mathbf{C}_v = \mathbf{A}\mathbf{v} \in \mathbb{R}^{n\times n}$where $\mathbf{C}_v$ is the circulant matrix constructed from $\mathbf{v}$