circulant matrix

A square matrixMathworldPlanetmath M:A×AC is said to be g-circulant for an integer g if each row other than the first is obtained from the preceding row by shifting the elements cyclically g columns to the right (g¿0) or -g columns to the left (g ¡ 0).

That is, if A=[aij] then ai,j=ai+1,j+g where the subscripts are computed modulo d. A 1-circulant is commonly called a circulant and a -1-circulant is called a back circulant.

More explicitly, a matrix of the form


is called circulant.

Because the Jordan decomposition ( of a circulant matrix is rather simple, circulant matrices have some interest in connection with the approximation of eigenvaluesMathworldPlanetmathPlanetmathPlanetmathPlanetmath of more general matrices. In particular, they have become part of the standard apparatus in the computerized analysis of signals and images.

Title circulant matrix
Canonical name CirculantMatrix
Date of creation 2013-03-22 13:53:38
Last modified on 2013-03-22 13:53:38
Owner bwebste (988)
Last modified by bwebste (988)
Numerical id 9
Author bwebste (988)
Entry type Definition
Classification msc 15-01
Classification msc 15A99