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Bob Hanlon
Bob Hanlon
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The code below is given in Eric Weisstein's Math World article: Matrix Minimal PolynomialMatrix Minimal Polynomial.

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}] ]

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}]
  ]

Is it possible to adapt the code to give the minimal polynomial of a matrix over a finite field of prime order $p$. Perhaps by adding Modulus -> pModulus -> p in the argument for NullSpaceNullSpace.

The code below is given in Eric Weisstein's Math World article: Matrix Minimal Polynomial.

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}] ]

Is it possible to adapt the code to give the minimal polynomial of a matrix over a finite field of prime order $p$. Perhaps by adding Modulus -> p in the argument for NullSpace.

The code below is given in Eric Weisstein's Math World article: Matrix Minimal Polynomial.

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}]
  ]

Is it possible to adapt the code to give the minimal polynomial of a matrix over a finite field of prime order $p$. Perhaps by adding Modulus -> p in the argument for NullSpace.

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geoffrey
geoffrey
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Find the minimal polynomial for a matrix over a finite field

The code below is given in Eric Weisstein's Math World article: Matrix Minimal Polynomial.

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}] ]

Is it possible to adapt the code to give the minimal polynomial of a matrix over a finite field of prime order $p$. Perhaps by adding Modulus -> p in the argument for NullSpace.