Difference between revisions of "Manuals/calci/CIRCULANT"
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(Created page with "<div style="font-size:30px">'''CIRCULANT'''</div><br/>") |
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| − | <div style="font-size:30px">'''CIRCULANT'''</div><br/> | + | <div style="font-size:30px">'''MATRIX("CIRCULANT",order)'''</div><br/> |
| + | *<math>order</math> 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. | ||
| + | 8Circulant matrices are very useful in digital image processing, and the n×n circulant matrix is implemented as CirculantMatrix. | ||
Revision as of 06:39, 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
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.
8Circulant matrices are very useful in digital image processing, and the n×n circulant matrix is implemented as CirculantMatrix.