M = Matrix.New({{1,1,1,1,1,1},
                {1,1,2,3,4,5},
                {1,2,3,4,8,6},
                {1,3,4,5,6,7},
                {1,4,8,6,7,8},
                {1,5,6,7,8,1}})
G1, U1 = Matrix.Tridiagonalize(M,{{"BlockSize",1}})
G2, U2 = Matrix.Tridiagonalize(M,{{"BlockSize",2}})

print("The matrix M in tri-diagonal form is")
print(ResponseFunction.ToMatrix(G1))
print("The unitary matrix U1 that transforms M to tridiagonal form is given as")
print(U2)
print("And if we look at U^**M*U^T we get")
print(Chop(U1*M*Matrix.Transpose(U1)))

print("The matrix M in Block tri-diagonal form is")
print(ResponseFunction.ToMatrix(G2))
print("The unitary matrix U2 that transforms M to tridiagonal form is given as")
print(U2)
print("And if we look at U^**M*U^T we get")
print(Chop(U2*M*Matrix.Transpose(U2)))