Definition:Circulant
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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