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how to get the transformation matrix for a transformation over 4x4 matrices?

I have the following transformation:

M = MatrixSpace(QQ,4,4)
def f(m):
    return matrix([
            [m[0][0], m[0][1], m[0][2], m[0][3]],
            [m[1][3], m[1][0], m[1][1], m[1][2]],
            [m[2][2], m[2][3], m[2][0], m[2][1]],
            [m[3][1], m[3][2], m[3][3], m[3][0]]
        ])
print linear_transformation(M, M, f)

This is not working - but I can't figure out what linear_transformation is expecting. How can I get this to work? Is this even possible?

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how to get the transformation matrix for a transformation over 4x4 matrices?

I have the following transformation:

M = MatrixSpace(QQ,4,4)
def f(m):
    return matrix([
            [m[0][0], m[0][1], m[0][2], m[0][3]],
            [m[1][3], m[1][0], m[1][1], m[1][2]],
            [m[2][2], m[2][3], m[2][0], m[2][1]],
            [m[3][1], m[3][2], m[3][3], m[3][0]]
        ])
print linear_transformation(M, M, f)

This is not working - but I can't figure out what linear_transformation is expecting. How can I get this to work? Is this even possible?

click to hide/show revision 3
retagged

how to get the transformation matrix for a transformation over 4x4 matrices?

I have the following transformation:

M = MatrixSpace(QQ,4,4)
def f(m):
    return matrix([
            [m[0][0], m[0][1], m[0][2], m[0][3]],
            [m[1][3], m[1][0], m[1][1], m[1][2]],
            [m[2][2], m[2][3], m[2][0], m[2][1]],
            [m[3][1], m[3][2], m[3][3], m[3][0]]
        ])
print linear_transformation(M, M, f)

This is not working - but I can't figure out what linear_transformation is expecting. How can I get this to work? Is this even possible?