OFFSET
1,1
COMMENTS
Determinant of the n times n matrix with T(n,n)=0 is equal to 1 for every such matrix. Tested up to n=13.
For elements where row index is greater than column index, every negative number appears to give a positive contribution while every positive number appears to give a negative contribution to the determinant of the matrix. The size of a such contribution appears to be 1 when replacing the number with a zero. [From Mats Granvik, Sep 22 2008]
LINKS
Solve My Math, Matrix Calculator.
E. W. Weisstein, Redheffer Matrix.
Wikipedia, Moebius Function Matrix.
EXAMPLE
Determinant of:
1
is equal to 1.
Determinant of:
1,1
-1,1
is equal to 2.
Determinant of:
1,1,1
-1,1,0
-1,0,1
is equal to 3.
Determinant of:
1,1,1,1
-1,1,0,0
-1,0,1,0
0,-1,0,1
is equal to 4.
Determinant of:
1,1,1,1,1
-1,1,0,0,0
-1,0,1,0,0
0,-1,0,1,0
-1,0,0,0,1
is equal to 5.
Determinant of:
1,1,1,1,1,1
-1,1,0,0,0,0
-1,0,1,0,0,0
0,-1,0,1,0,0
-1,0,0,0,1,0
1,-1,-1,0,0,1
is equal to 6.
Determinant of:
1,1,1,1,1,1,1
-1,1,0,0,0,0,0
-1,0,1,0,0,0,0
0,-1,0,1,0,0,0
-1,0,0,0,1,0,0
1,-1,-1,0,0,1,0
-1,0,0,0,0,0,1
is equal to 7.
PROG
CROSSREFS
KEYWORD
tabl,sign
AUTHOR
STATUS
approved