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/>
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<div style="font-size:30px">'''MATRIX("REDHEFFER",order)'''</div><br/>
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*<math>order</math> is the size of the Redheffer matrix.
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==Description==
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*This function gives the redheffer matrix of order 3.
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*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
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<math>\begin{bmatrix}
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1 \\
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\end{bmatrix}</math>
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<math>\begin{bmatrix}
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1 & 1 \\
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1 & 1 \\
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\end{bmatrix}</math>
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<math>\begin{bmatrix}
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1 & 1  & 1 \\
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1 & 1  & 0 \\
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1 & 0 & 1 \\
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\end{bmatrix}</math>
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<math>\begin{bmatrix}
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1 & 1  & 1  & 1 \\
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1 & 1  & 0  & 1 \\
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1 & 0 & 1 & 0  \\
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1 & 0 & 0 & 1 \\
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\end{bmatrix}</math>
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*The determinant of the n×n Redheffer matrix is equal to the Mertens function M(n).
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==Examples==
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*1.MATRIX("redheffer")
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{| class="wikitable"
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|-
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| 1 || 1 || 1
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|-
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| 1 || 1 || 0
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|-
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| 1 || 0 || 1
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|}
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*2.MATRIX("redheffer",6)
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{| class="wikitable"
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|-
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| 1 || 1 || 1 || 1 || 1 || 1
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|-
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| 1 || 1 || 0 || 1 || 0 || 1
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|-
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| 1 || 0 || 1 || 0 || 0 || 1
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|-
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| 1 || 0 || 0 || 1 || 0 || 0
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|-
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| 1 || 0 || 0 || 0 || 1 || 0
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|-
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| 1 || 0 || 0 || 0 || 0 || 1
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|}
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==See Also==
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*[[Manuals/calci/ANTIDIAGONAL| ANTIDIAGONAL]]
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*[[Manuals/calci/CONFERENCE| CONFERENCE]]
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*[[Manuals/calci/CIRCULANT| CIRCULANT]]
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*[[Manuals/calci/HANKEL| HANKEL]]
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==References==

Revision as of 12:58, 30 April 2015

MATRIX("REDHEFFER",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 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 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

See Also


References