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A circulant matrix is a square matrix where each row has the same elements as the previous row, cyclically rotated right by one element. It is a specific kind of a square Toeplitz matrix.

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Define circulant matrix using matrix-vector multiplication?

The map is $$ L(a_1\,\ldots,a_n) = \sum_{ i=1}^n a_i L\mathbb{e}_i, $$ with $ L \mathbb{e}_i \in \mathbb{R}^{n\times n} $ given by $$ (L\mathbb{e}_i)\mathbb{e}_q\cdot \mathbb{e}_p = \begin{cases} 1 &\ …
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