A circulant matrix is a Toeplitz matrix with the additional property [t.
MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (), which on the fine level in the case of a 1-level circulant matrix of even size is given by
the sum of circulant matrices of the s ame type is a circulant matrix of the same type,
The product of a left circulant and a right circulant is a left circulant matrix.
We observe that the adjacency matrix of the Knodel graphs is a (-1) circulant matrix
, called also a retrocirculant , where all the rows are circular permutations of the first row toward left.
In can be seen easily from the above definition that the circulant matrix
n]) which yields a circulant matrix
that can be diagonalized by the discrete Fourier transform (DFT) .
Periodic boundary conditions imply that the image repeats itself endlessly in all directions; periodic boundary conditions imply that H is a block circulant matrix
with circulant blocks (BCCB).
A right circulant matrix
with Perrin sequenc is a matrix of the form
A is a circulant matrix
of size n generated by the function f whose Fourier coefficients form the PSF.
nxn](R) is said to be a right circulant matrix
if it is of the form
The unit circulant matrix
Z can be diagonalized by the Fourier unitary matrix [OMEGA] = ([w.