1,3

Index entries for sequences related to binary matrices

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).

Cf. other counts for (0, 1) matrices: A003024 positive eigenvalues, A055165 nonsingular, A085656 positive definite.

Sequence in context: A006179 A029809 A093252 this_sequence A068255 A157280 A070908

Adjacent sequences: A098145 A098146 A098147 this_sequence A098149 A098150 A098151

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Hugo Pfoertner (hugo(AT)pfoertner.org), Sep 07 2004