I am trying to write the code for Optimization of the matrix completion model from the textbook for my practice

The matrix completion problem in (9.21) can be solved following an alternating min imization approach. in a similar sense as with Kmeans. The gradient of the objective function g (C, W} = Z (c'lw; xgjf with respect to the pth column of W is given by (if! ER pr3 = 2 2 (6w? xtp) (3)1". (9.22} times: Setting the gradient to zero, we can recover the optimal wp by solving the following linear system of equations: 2 cl [elf wp = Z x;_,, (elf. (9.23} (men men Similarly, the optimal C\" can be found as a solution to e" E ijf = Z xjw}. (9.24} (NJ! 69 (nun en By alternately solving these linear system until the values of C and W do not change very much we can solve (9.21)