# 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.

50 questions
1answer
29 views

### What is the decomposition of $H^{T}H$, when $H$ is a circulant matrix?

Since $H$ is a circulant matrix, the decomposition using Fourier transform matrix $F$ $$H = F^{-1} \Lambda F$$ where $\Lambda$ is the diagonal matrix with the eigenvalues of $H$. If I plug in the ...
0answers
35 views

### Circulant matrix-vector product procedure

A circulant matrix $C$ can be represented as $$C = F^{-1} \mbox{diag}(Fc) \, F$$ When $C$ is multiplied by vector $b$ $$C b = F^{-1} \mbox{diag}(Fc) \, (F b)$$ My question only about procedure. ...
0answers
27 views

0answers
23 views

### Does a square root matrix of a circulant correlation matrix with positive entries also have all positive entries?

I have a circulant correlation matrix that has only positive entries. (Because it is a correlation matrix, it is symmetric with diagonal entries of 1.) I am wondering about the entries of the square ...
1answer
30 views

1answer
55 views

### Eigenvalues of product of two vectors and circulant matrix

I have the following matrix: $$A_{ij} = B_{ij} C_{ij} = v_i v_j C_{ij}$$ where $v$ is a vector of wavenumbers and $C$ is a circulant matrix. I want to find the eigenvalues/vectors of $A$. The matrix ...
1answer
55 views

2answers
18 views

0answers
24 views

### Diagonalizing classes of matrix

I know that the class of circulant matrices is diagonalized by the Discrete Fourier Transform Matrix. Are there other any such classes of matrices diagonalized by other well-known matrices?
1answer
94 views

### What is the Diameter of the outer Circle formed by 3-inner circles which Thicknes-wide is 1.25 mts? see dranw. Thank you [closed]

What is the Diameter of the outer Circle formed by 3-inner circles which Thickness-wide is 1.25 mts? see drawn. Thank you
2answers
277 views

### Eigenvalues of Circulant Matrix

I am studying about circulant matrices, and I have seen that one of the properties of such matrices is the eigenvalues which are some combinations of roots of unity. I am trying to understand why it ...
0answers
104 views

### Circulant Orthogonal $\operatorname{MDS}$ Matrix

Definition: A matrix $M$ of order $n$ over a field is a $\operatorname{MDS}$ matrix if and only if every sub-matrix of $M$ is non-singular. My question: How to proof the following statement. If $A$ ...
1answer
245 views

### Number of invertible circulant matrices over a finite field

As far as I can tell, the basic results on circulant matrices (traditionally carried out over $\mathbb{C}$) are still true over a finite field $F$ as long as you have "enough" roots of unity. The ...
0answers
130 views

### Creating a 3 dimensional circulant matrix from a 3 dimensional block Toeplitz matrix

As a preemptive apology I am a physics undergrad so the maths I am using is beyond what I am used to seeing and after a few hours of hunting I am struggling to find an answer. The problem I am ...
0answers
47 views