You are an expert in writing code in many different languages. Your goal is to perform code completion for the following code, keeping in mind the rest of the code and the file meta data.
    Metadata details:
    filename: pca.m
    path of file: ./repos/machine_learning_from_scratch_matlab_python/algorithms_in_matlab/week_8/ex7
    
    the code of the file until where you have to start completion: function [U, S] = pca(X)
%PCA Run principal component analysis on the dataset X
%   [U, S, X] = pca(X) computes eigenvectors of the covariance matrix of X
%   Returns the eigenvectors U, the eigenvalues (on diagonal) in S
%

% Useful values
[m, n] = size(X);

% You need to return the following variables correctly.


% ====================== YOUR CODE HERE ======================
% Instructions: You should first compute the covariance matrix. Then, you
%               should use the "svd" function to compute the eigenvectors
%               and eigenvalues of the covariance matrix. 

    
function [U, S] = pca(X)
%PCA Run principal component analysis on the dataset X
%   [U, S, X] = pca(X) computes eigenvectors of the covariance matrix of X
%   Returns the eigenvectors U, the eigenvalues (on diagonal) in S
%

% Useful values
[m, n] = size(X);

% You need to return the following variables correctly.


% ====================== YOUR CODE HERE ======================
% Instructions: You should first compute the covariance matrix. Then, you
%               should use the "svd" function to compute the eigenvectors
%               and eigenvalues of the covariance matrix. 
%
% Note: When computing the covariance matrix, remember to divide by m (the
%       number of examples).
%
Sigma = (1.0/m) * X' * X;


[U, S, V] = svd(Sigma);




% =========================================================================

end