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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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How to determine if there exists a non-zero vector in the kernel

Let $C$ denote your circulant matrix and $P$ the cyclic permutation matrix as defined in http://en.wikipedia.org/wiki/Circulant_matrix such that $P^n=I$ is the identity matrix. After rotating the fir …
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