Search: id:A098148
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%I A098148
%S A098148 0,0,52,22196,21012607
%N A098148 Number of real (0,1) n X n matrices such that some eigenvalues are strictly 
               complex.
%H A098148 <a href="Sindx_Mat.html#binmat">Index entries for sequences related to 
               binary matrices</a>
%e A098148 The 3 X 3 matrix ((0,1,0),(0,0,1),(1,1,1)) has real eigenvalue 1.83929 
               and the complex pair -0.41964+-0.60629*i. There are 12 (0,1) 3 X 
               3 matrices with these eigenvalues. There are 6 groups of 6 matrices 
               having eigenvalues (1.3472,-0.66236+-0.56228*i), (1.46557,-0.23279+-0.79255*i),
               ..., (2.32472,0.33764+-0.56228*i). Two matrices (e.g. ((0,0,1),(1,
               0,0),(0,1,0)) ) have eigenvalues (1,-0.5+-0.5*sqrt(3)*i). Two matrices 
               (e.g. ((1,1,0),(0,1,1),(1,0,1)) ) have eigenvalues (2,0.5+-0.5*sqrt(3)*i). 
               Total: 12+6*6+2+2=52=a(3).
%Y A098148 Cf. other counts for (0, 1) matrices: A003024 positive eigenvalues, A055165 
               nonsingular, A085656 positive definite.
%Y A098148 Sequence in context: A006179 A029809 A093252 this_sequence A068255 A157280 
               A070908
%Y A098148 Adjacent sequences: A098145 A098146 A098147 this_sequence A098149 A098150 
               A098151
%K A098148 more,nonn
%O A098148 1,3
%A A098148 Hugo Pfoertner (hugo(AT)pfoertner.org), Sep 07 2004

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