Manuals/calci/CIRCULANT

MATRIX("CIRCULANT",order)

• $order$ is the order of the arrowhead matrix.

Description

• This function gives the Circulant matrices of given order.
• A circulant matrix is a special kind of Toeplitz matrix where each row vector is rotated one element to the right relative to the preceding row vector.
• An n × n circulant matrix is formed from any n vector by cyclically permuting the entries.
• Starting with [a b c] we can generate the 3 × 3 circulant matrix

$C={\begin{vmatrix}a&b&c\\c&a&b\\b&c&a\\\end{vmatrix}}$.

• Here MATRIX("circulant") is giving the circulant matrix for random numbers in decimal.
• Circulant matrices are very useful in digital image processing, and the n×n circulant matrix is implemented as CirculantMatrix.