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REFERENCES
| R. A. Horn and C. R. Johnson, Matrix Analysis, Cambridge, 1988, Section 1.3.
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MATHEMATICA
| Needs["Utilities`FilterOptions`"] Options[DiagonalizableQ]={ Field->Complexes, ZeroTest->(RootReduce[ # ]===0&) };
Matrices[n_, l_List:{0, 1}] := Partition[ #, n]&/@Flatten[Outer[List, Sequence@@Table[l, {n^2}]], n^2-1]
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] ] ]
Table[Count[Matrices[n], _?DiagonalizableQ], {n, 4}]
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