Manuals/calci/CIRCULANT
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MATRIX("CIRCULANT",order)
- Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle order} is the order of the circulant 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
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle C =\begin{vmatrix} a & b & c \\ c & a & b \\ b & c & a \\ \end{vmatrix}} .
- In Calci, 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.
Examples
- MATRIX("circulant")= 0.793114245403558
- MATRIX("circulant",3)
| 0.15551561512984335 | 0.43306124373339117 | 0.7585938205011189 |
| 0.7585938205011189 | 0.15551561512984335 | 0.43306124373339117 |
| 0.43306124373339117 | 0.7585938205011189 | 0.15551561512984335 |
- MATRIX("circulant",5,20..100..15)
| 20 | 80 | 65 | 50 | 35 |
| 35 | 20 | 80 | 65 | 50 |
| 50 | 35 | 20 | 80 | 65 |
| 65 | 50 | 35 | 20 | 80 |
| 80 | 65 | 50 | 35 | 20 |