Difference between revisions of "Manuals/calci/CIRCULANT"
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*An n × n circulant matrix is formed from any n vector by cyclically permuting the entries. | *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 | *Starting with [a b c] we can generate the 3 × 3 circulant matrix | ||
| − | C =\begin{vmatrix} | + | <math>C =\begin{vmatrix} |
a & b & c \\ | a & b & c \\ | ||
c & a & b \\ | c & a & b \\ | ||
b & c & a \\ | b & c & a \\ | ||
| − | \end{vmatrix} | + | \end{vmatrix}</math>. |
*Here MATRIX("circulant") is giving the circulant matrix for random numbers in decimal. | *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. | |
Revision as of 06:40, 18 April 2015
MATRIX("CIRCULANT",order)
- is the order of the arrowhead matrix.
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
.
.
- 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.