# Questions tagged [circulant-matrices]

For questions regarding circulant matrices, where each row vector is rotated one element to the right relative to the preceding row vector.

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### Find the $n$th power of a 3-by-3 circulant matrix

Consider the matrix given as $$A=\begin{bmatrix}a_0 & a_2 & a_1\\ a_1 & a_0 & a_2\\ a_2 & a_1 & a_0\end{bmatrix}$$ Write a formula for $A^n$ for $n\in\mathbb{N}$.  My ...
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### Circulant determinant factorization over Z

Let $X_n= \begin{bmatrix} x_1&x_2&\cdots&x_n\\ x_n&x_1&\cdots&x_{n-1}\\ \vdots&\vdots&\ddots&\vdots\\ x_2&x_3&\cdots&x_1\\ \end{bmatrix}$ be a ...
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### Measuring real square matrix's deviation from being circulant?

What metrics or measurements exist for determining how much a (real square) matrix deviates from being circulant?
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### Generating doubly block circulant matrices which are also symmetric positive definite

I have generated in python some matrices with doubly block circulant structure (i.e. also the blocks themselves are circulant). These matrices are square, sparse and with coefficient drawn from ...
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### Can an arbitrary diagonal matrix be used to generate a 3 level circulant matrix?

From here, we know the BCCB (block circulant with circulant blocks, a 2 level circulant matrix) can be diagonalized by the Fourier basis. The references therein actually tell us this is true in ...