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A085656
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Number of positive-definite real {0,1} n X n matrices.
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9
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OFFSET
| 1,2
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COMMENTS
| A real matrix M is positive-definite if x M x' > 0 for all nonzero real vectors x. Equivalently, all eigenvalues of M + M' are positive.
M need not be symmetric. For the number of different values of M + M' see A085657. - Max Alekseyev (maxale(AT)gmail.com), Dec 13 2005
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LINKS
| Index entries for sequences related to binary matrices
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EXAMPLE
| For n = 2 the three matrices are {{{1, 0}, {0, 1}}, {{1, 0}, {1, 1}}, {{1, 1}, {0, 1}}}.
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PROG
| (PARI) { a(n) = M=matrix(n, n, i, j, 2*(i==j)); r=0; b(1); r } { b(k) = local(t); if(k>n, t=0; for(i=1, n, for(j=1, i-1, if(M[i, j]==1, t++); )); r+=2^t; return; ); forvec(x=vector(k-1, i, [0, 1]), for(i=1, k-1, M[k, i]=M[i, k]=x[i]); if( matdet(vecextract(M, 2^k-1, 2^k-1), 1)>0, b(k+1) ) ) } (Alekseyev)
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CROSSREFS
| Cf. A055165, which counts nonsingular {0, 1} matrices and A085506, which counts {-1, 0, 1} matrices with positive eigenvalues.
Cf. A085657, A085658, A086215, A038379 (positive semi-definite matrices), A080858, A083029.
Sequence in context: A062496 A185237 A099084 * A113100 A038379 A047656
Adjacent sequences: A085653 A085654 A085655 * A085657 A085658 A085659
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KEYWORD
| nonn,nice
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), Jul 12 2003
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EXTENSIONS
| More terms from Max Alekseyev (maxale(AT)gmail.com), Dec 13 2005
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