Definition:Circulant

Definition

A circulant is a matrix or a determinant with the following properties:

$(1): \quad$ Every row is a cyclic permutation of the row above it

$(2): \quad$ The diagonal elements are all the same.

Examples

Arbitrary Example

This is an example of a circulant:

$\begin {pmatrix} a & b & c & d \\ d & a & b & c \\ c & d & a & b \\ b & c & d & a \end {pmatrix}$

Also see

• Results about circulants can be found here.

Sources

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): circulant
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): circulant