The circulant-matrices tag has no wiki summary.

**0**

votes

**0**answers

20 views

### How to fast calculate the main diagonal elements of a matrix which is a product of several circulant matrices and diagonal matrices?

Suppose that $\mathbf H$ is an $L\times L$ circulant matrix, and $\mathbf v$ and $\mathbf x$ are $L\times 1$ column vectors. As we know, $\mathbf H \mathbf x$ can calculated by FFT with a computation ...

**7**

votes

**1**answer

468 views

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

If you are given a $0$-$1$ circulant matrix with $n$ rows and $n$ columns, is there an efficient way of determining if there exists a non-zero $\{-1,0,1\}$-vector in its kernel?
Could this problem ...

**0**

votes

**1**answer

102 views

### Graphs with circulant distance matrices

The cycle has this property. For instance, the distance matrix for a 6-cycle is:
$A=\begin{bmatrix}
0 & 1 & 2 & 3 & 2 & 1 \\\\
1 & 0 & 1 ...

**1**

vote

**0**answers

114 views

### bounds on the entries of an inverse circulant matrix

Suppose that $C$ is a (real) circulant invertible matrix defined by a vector $d$. Then $C^{-1}$ is also a circulant defined by some vector $f$. There exists a standard formula that expresses the ...