A086899
Number of real n X n invertible symmetric (0,1) matrices.
Original entry on oeis.org
1, 4, 32, 528, 18596, 1280468, 180452552, 49970930912, 27618771417328, 30088644932329872
Offset: 1
For n = 2 the 4 matrices are 10/01, 01/10, 11/10, 01/11.
-
triamat[li_List] := (*see A086900*); Table[it=triamat/@IntegerDigits[Range[0, -1+2^(n(n+1)/2)], 2, n(n+1)/2]; Count[it, (q_)?MatrixQ/;(Det[q]=!=0)], {n, 5}]
A118993
Number of real n X n symmetric (+1,-1) matrices with nonzero permanent.
Original entry on oeis.org
2, 4, 64, 832, 23808, 1725952, 268435456, 64638447616, 33770336417792
Offset: 1
A118994
Number of real n X n symmetric (+1,-1) matrices with positive determinant.
Original entry on oeis.org
1, 0, 16, 432, 8448, 282240, 81949952, 32715189248, 12792558313472, 9318420858593280
Offset: 1
-
F:= proc(n) local Q,q,X,x,t,A,ii,L,v;
Q:= [[1,1],seq(seq([i,j],i=2..j),j=2..n)];
q:= nops(Q);
X:= [seq(x[q[1],q[2]],q=Q)];
t:= 0:
A:= Matrix(n,n,shape=symmetric,symbol=x);
A[2..n,1]:= Vector(n-1,1);
for ii from 0 to 2^q-1 do
L:= map(s -> 2*s-1, convert(2^q+ii,base,2)[1..q]);
v:= LinearAlgebra:-Determinant(subs(zip(`=`,X,L),A));
if v > 0 then t:= t+1 fi
od;
2^(n-1)*t;
end proc:
seq(F(n),n=1..7); # Robert Israel, Apr 14 2016
A118997
Number of real n X n symmetric (+1,-1) matrices with negative determinant.
Original entry on oeis.org
1, 4, 16, 80, 8448, 907904, 81949952, 13480664064, 12792558313472, 18963201072750592
Offset: 1
A118990
Number of symmetric singular n X n (+1,-1) matrices over the reals.
Original entry on oeis.org
0, 4, 32, 512, 15872, 907008, 104535552, 22523623424, 9599255461888, 7747175087620096
Offset: 1
Showing 1-5 of 5 results.