M=(({{2, 4, -6, 0}, {4, 6, -3, -4}, {0, 0, 4, 0}, {0, 4, -6, 2}}))

Eigenvalues[M]

NullSpace[M - 6*IdentityMatrix[4]]

NullSpace[M - 4*IdentityMatrix[4]]

NullSpace[M - 2*IdentityMatrix[4]]

NullSpace[MatrixPower[M - 2*IdentityMatrix[4], 2]]

(M - 2*IdentityMatrix[4]) . {-1, 1, 0, 0}

S = {{1, 1, 0, 1}, {0, 3, 2, 0}, {1, 0, 0, 1}, {-1/4, 1/4, 0, 
          0}}

T = Transpose[S]

J = Inverse[T] . M . T

MatrixForm[J]