Find the minimal polynomial for the square matrix a in the variable x

hbghlyj

MatrixMinimalPolynomial[a_List?MatrixQ,x_]:=Module[
    {
      i,
      n=1,
      qu={},
      mnm={Flatten[IdentityMatrix[Length[a]]]}
    },
    While[Length[qu]==0,
      AppendTo[mnm,Flatten[MatrixPower[a,n]]];
      qu=NullSpace[Transpose[mnm]];
      n++
    ];
    First[qu].Table[x^i,{i,0,n-1}]
  ]

Mathworld