Manuals/calci/REDHEFFER - Revision history

Devika: /* Examples */

2015-10-26T07:37:51Z

Examples

2015-05-15T16:19:27Z

2015-04-30T17:58:04Z

2015-04-30T05:28:04Z

Created page with "<div style="font-size:30px">'''REDHEFFER'''</div><br/>"

New page

<div style="font-size:30px">'''REDHEFFER'''</div><br/>

@@ Line 26: / Line 26: @@
 ==Examples==
-*1.MATRIX("redheffer")
+*1.MATRIX("redheffer") =1
 {| class="wikitable"
 |-
@@ Line 35: / Line 36: @@
 | 1 || 0 || 1
 |}
-*2.MATRIX("redheffer",6)
+*3.MATRIX("redheffer",6)
 {| class="wikitable"
 |-

@@ Line 56: / Line 56: @@
 *[[Manuals/calci/CIRCULANT| CIRCULANT]]
 *[[Manuals/calci/HANKEL| HANKEL]]
 ==References==

← Older revision		Revision as of 17:58, 30 April 2015
Line 1:		Line 1:
−	<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")
		+	{\| class="wikitable"
		+	\|-
		+	\| 1 \|\| 1 \|\| 1
		+	\|-
		+	\| 1 \|\| 1 \|\| 0
		+	\|-
		+	\| 1 \|\| 0 \|\| 1
		+	\|}
		+	*2.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==