Write the Matrix2 by using Matrix1

[quest]

I think you are way down the rabbit hole of "How do I do this" when I have serious doubts that this is something you need to do. Why do you have 64 rho variables instead of a rho list? If you had a rho list you could reshape it to fit your needs.

Of course I had to give it a try since it looks like a fun problem.

class RefMatrix():
    def __init__(self, ref):
        self.ref = ref
        self.indices = []
        self.rows = len(ref)
        self.columns = len(ref[0])
        self._values = []
        for r in range(self.rows):
            self.indices.append([(r, c) for c in range(self.columns)])
            self._values.append([0]*self.columns)

    def values(self):
        for r, row in enumerate(self.indices):
            for c, index in enumerate(row):
                self._values[r][c] = self.ref[index[0]][index[1]]
        return self._values

    def swapRows(self, a, b):
        self.indices[a], self.indices[b] = self.indices[b], self.indices[a]
        return self

    def swapColumns(self, a, b):
        for row in self.indices:
            row[a], row[b] = row[b], row[a]
        return self

data = [[r*4+c for c in range(4)] for r in range(4)]
ref = RefMatrix(data).swapRows(2, 3).swapColumns(2, 3)
print(data)
print(ref.values())

Output:
[[0, 1, 2, 3], [4, 5, 6, 7], [8, 9, 10, 11], [12, 13, 14, 15]]
[[0, 1, 3, 2], [4, 5, 7, 6], [12, 13, 15, 14], [8, 9, 11, 10]]

thanks for answer,
will also try this way after make other way run correctly. but the main point I am multiplying this rho symbolic matrices with other real matrices. This is why I had to use sympy. Otherwise, it is not possible to multiply a real matrix with a symbolic matrix