1,1

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 O. Granvik (mgranvik(AT)abo.fi), Sep 22 2008]

Solve My Math, Matrix Calculator.

E. W. Weisstein, Redheffer Matrix.

Wikipedia, Moebius Function Matrix.

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.

(Excel cell formula) =if(mod(row(); column())=0; lookup(row()/column(); A000027; A008683); if(row()=1; 1; 0))

Cf. A008683, A143104, A000027.

Cf. A054525. [From Mats O. Granvik (mgranvik(AT)abo.fi), Sep 21 2008]

Sequence in context: A127247 A127244 A144778 this_sequence A111940 A129572 A070950

Adjacent sequences: A143139 A143140 A143141 this_sequence A143143 A143144 A143145

tabl,sign

Mats O. Granvik, Gary W. Adamson and Roger L. Bagula (mgranvik(AT)abo.fi), Jul 27 2008, Sep 21 2008