Search: id:A091472
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%I A091472
%S A091472 2,12,320,43892
%N A091472 Number of n X n matrices with entries {0,1} that are diagonalizable over 
               the complex numbers.
%C A091472 A matrix M is diagonalizable over a field F if there is an invertible 
               matrix S with entries from F such that S^(-1) M S is diagonal.
%C A091472 An n X n matrix M is diagonalizable if and only if it has n linearly 
               independent eigenvectors.
%D A091472 R. A. Horn and C. R. Johnson, Matrix Analysis, Cambridge, 1988, Section 
               1.3.
%H A091472 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               DiagonalizableMatrix.html">Diagonalizable Matrix</a>
%H A091472 <a href="Sindx_Mat.html#binmat">Index entries for sequences related to 
               binary matrices</a>
%e A091472 a(2) = 12: all except 00/10, 01/00, 11/01, 10/11.
%t A091472 Needs["Utilities`FilterOptions`"] Options[DiagonalizableQ]={ Field->Complexes, 
               ZeroTest->(RootReduce[ # ]===0&) };
%t A091472 Matrices[n_, l_List:{0, 1}] := Partition[ #, n]&/@Flatten[Outer[List, 
               Sequence@@Table[l, {n^2}]], n^2-1]
%t A091472 DiagonalizableQ[m_List?MatrixQ, opts___] := Module[ { field=Field/.{opts}/
               .Options[DiagonalizableQ], eigenopts=FilterOptions[Eigenvectors, 
               opts] }, Switch[field, Complexes, ComplexDiagonalizableQ[m, eigenopts], 
               Reals, RealDiagonalizableQ[m, eigenopts] ] ]
%t A091472 Table[Count[Matrices[n], _?DiagonalizableQ], {n, 4}]
%Y A091472 Cf. A091470, A091471.
%Y A091472 Sequence in context: A012422 A122767 A094047 this_sequence A156518 A012727 
               A088229
%Y A091472 Adjacent sequences: A091469 A091470 A091471 this_sequence A091473 A091474 
               A091475
%K A091472 nonn,more
%O A091472 1,1
%A A091472 Eric Weisstein (eric(AT)weisstein.com), Jan 12, 2004

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