Difference between revisions of "Manuals/calci/REDHEFFER"
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*[[Manuals/calci/CIRCULANT| CIRCULANT]] | *[[Manuals/calci/CIRCULANT| CIRCULANT]] | ||
*[[Manuals/calci/HANKEL| HANKEL]] | *[[Manuals/calci/HANKEL| HANKEL]] | ||
| − | |||
==References== | ==References== | ||
| + | *[http://en.wikipedia.org/wiki/Redheffer_matrix Redheffer Matrix] | ||
Revision as of 10:19, 15 May 2015
- 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 size of the Redheffer matrix.
Description
- This function gives the redheffer matrix of order 3.
- A Redheffer matrix is a square (0,1) -matrix with elements 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 a_(ij)} equal to 1 if j=1 or i/j (i divides j), and 0 otherwise. *For n=1, 2, ..., The first few Redheffer matrices are
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 \begin{bmatrix} 1 \\ \end{bmatrix}} 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 \begin{bmatrix} 1 & 1 \\ 1 & 1 \\ \end{bmatrix}} 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 \begin{bmatrix} 1 & 1 & 1 \\ 1 & 1 & 0 \\ 1 & 0 & 1 \\ \end{bmatrix}} 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 \begin{bmatrix} 1 & 1 & 1 & 1 \\ 1 & 1 & 0 & 1 \\ 1 & 0 & 1 & 0 \\ 1 & 0 & 0 & 1 \\ \end{bmatrix}}
- The determinant of the n×n Redheffer matrix is equal to the Mertens function M(n).
Examples
- 1.MATRIX("redheffer")
| 1 | 1 | 1 |
| 1 | 1 | 0 |
| 1 | 0 | 1 |
- 2.MATRIX("redheffer",6)
| 1 | 1 | 1 | 1 | 1 | 1 |
| 1 | 1 | 0 | 1 | 0 | 1 |
| 1 | 0 | 1 | 0 | 0 | 1 |
| 1 | 0 | 0 | 1 | 0 | 0 |
| 1 | 0 | 0 | 0 | 1 | 0 |
| 1 | 0 | 0 | 0 | 0 | 1 |