# 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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### Determinant of circulant $(0,1)$ matrices of certain form

I am interested in computing the determinant of the following circulant matrices: let $n=p^k$ for $p$ a prime and $k\in \mathbb{N}$, take $a\in \mathbb{N}$ to be such that $a<p$ and $(a,p)=1$. ...
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### Diagonalize matrix of linear operator

Let $f : \mathbb{C} \to \mathbb{C}$ linear map such $$f(e_{i}) = \begin{cases} e_{i+1} & 1 \leq i<n \\ e_{1} & i=n\end{cases}$$ Diagonalize $f$. Thoughts I know the characteristic ...
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### inverting a tridiagonal circulant matrix with alternating elements

First of all, I want to underline that my knowledge regarding matrices is extremely restricted.. It just so happens that they are popping out everywhere in a recent project of mine. So, in this ...
1 vote
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### Operations with Circulant Matrix using GAP

I am newbie using GAP software. I need to know how to use GAP software for algebraic computations with circulant matrix. Some examples would suffice. Just for clarity Circulant Matrix: In linear ...
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### results of calculating eigenvalues and eigenvectors of permutation matrix

My question is actually about the derivation of eigenvalues and eigenvectors of the circulant matrix. I am not good at doing that in a straight way, i.e. calculating them with a general form of ...
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### Diagonalizing a matrix with 4 circulant blocks

I have the following matrix: $$\mathbf{M} = \begin{pmatrix} G_{1}^{(N)} & G_{2}^{(N)} \\ G_{2}^{(N)} & G_{3}^{(N)} \end{pmatrix}$$, where $G^{(N)}_{j}$ are symmetric circulant matrices of size ...
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### The square root of symmetric and circulant matrix is symmetric

Let $A$ a circulant symmetric matrix. From the definition of $\sqrt{A}$ it follows that also $\sqrt{A}$ is symmetric ( and circulant ). How can I show the symmetry without using the concept of ...
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### Efficient product of vector with inverse of positive definite circulant matrix plus real diagonal matrix?

Question: Hi! Would anyone happen to know an efficient way to compute: $$u^\top [C + D]^{-1},$$ where: $C$ is a square matrix, and is real, positive definite, and circulant $C$ is too large to fit ...
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