Manuals/calci/REDHEFFER

MATRIX("REDHEFFER",order)

• $order$ 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 $a_{(}ij)$ 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

${\begin{bmatrix}1\\\end{bmatrix}}$ ${\begin{bmatrix}1&1\\1&1\\\end{bmatrix}}$ ${\begin{bmatrix}1&1&1\\1&1&0\\1&0&1\\\end{bmatrix}}$ ${\begin{bmatrix}1&1&1&1\\1&1&0&1\\1&0&1&0\\1&0&0&1\\\end{bmatrix}}$

• The determinant of the n×n Redheffer matrix is equal to the Mertens function M(n).

Examples

• 1.MATRIX("redheffer") =1
• 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

See Also

• ANTIDIAGONAL
• CONFERENCE
• CIRCULANT
• HANKEL

References

• Redheffer Matrix