Difference between revisions of "Manuals/calci/REDHEFFER"
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(Created page with "<div style="font-size:30px">'''REDHEFFER'''</div><br/>") |
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| − | <div style="font-size:30px">'''REDHEFFER'''</div><br/> | + | <div style="font-size:30px">'''MATRIX("REDHEFFER",order)'''</div><br/> |
| + | *<math>order</math> 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 <math>a_(ij)</math> 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 | ||
| + | <math>\begin{bmatrix} | ||
| + | 1 \\ | ||
| + | \end{bmatrix}</math> | ||
| + | <math>\begin{bmatrix} | ||
| + | 1 & 1 \\ | ||
| + | 1 & 1 \\ | ||
| + | \end{bmatrix}</math> | ||
| + | <math>\begin{bmatrix} | ||
| + | 1 & 1 & 1 \\ | ||
| + | 1 & 1 & 0 \\ | ||
| + | 1 & 0 & 1 \\ | ||
| + | \end{bmatrix}</math> | ||
| + | <math>\begin{bmatrix} | ||
| + | 1 & 1 & 1 & 1 \\ | ||
| + | 1 & 1 & 0 & 1 \\ | ||
| + | 1 & 0 & 1 & 0 \\ | ||
| + | 1 & 0 & 0 & 1 \\ | ||
| + | \end{bmatrix}</math> | ||
| + | *The determinant of the n×n Redheffer matrix is equal to the Mertens function M(n). | ||
| + | |||
| + | ==Examples== | ||
| + | *1.MATRIX("redheffer") =1 | ||
| + | *2.MATRIX("redheffer",3) | ||
| + | {| class="wikitable" | ||
| + | |- | ||
| + | | 1 || 1 || 1 | ||
| + | |- | ||
| + | | 1 || 1 || 0 | ||
| + | |- | ||
| + | | 1 || 0 || 1 | ||
| + | |} | ||
| + | *3.MATRIX("redheffer",6) | ||
| + | {| class="wikitable" | ||
| + | |- | ||
| + | | 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 | ||
| + | |} | ||
| + | |||
| + | ==See Also== | ||
| + | *[[Manuals/calci/ANTIDIAGONAL| ANTIDIAGONAL]] | ||
| + | *[[Manuals/calci/CONFERENCE| CONFERENCE]] | ||
| + | *[[Manuals/calci/CIRCULANT| CIRCULANT]] | ||
| + | *[[Manuals/calci/HANKEL| HANKEL]] | ||
| + | |||
| + | ==References== | ||
| + | *[http://en.wikipedia.org/wiki/Redheffer_matrix Redheffer Matrix] | ||
Latest revision as of 02:37, 26 October 2015
MATRIX("REDHEFFER",order)
- is the size of the Redheffer matrix.
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 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
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
- The determinant of the n×n Redheffer matrix is equal to the Mertens function M(n).
Examples
- 1.MATRIX("redheffer") =1
- 2.MATRIX("redheffer",3)
| 1 | 1 | 1 |
| 1 | 1 | 0 |
| 1 | 0 | 1 |
- 3.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 |