I am studying PCA from Andrew Ng's Coursera cource and other material to visualize high dimensional vectors.

From the Stanford NLP course cs224n's first assignment, and lecture video from Andrew Ng.

They do SVD not Eigenvector decomposition to covariance matrix, and he even says that SVD is numerically more stable than Eig.

From my understanding, we should do SVD to data matrix(m,n), not covariance matrix(n,n). And eigenvector decomposition to covariance matrix.

Why do they do SVD to covariance matrix, not data matrix?

I even checked whether np.linalg.svd() is for covariance matrix, but it was for data matrix.

What happened?

I am studying PCA from Andrew Ng's Coursera course and other materials. In the Stanford NLP course cs224n's first assignment, and in the lecture video from Andrew Ng, they do singular value decomposition instead of eigenvector decomposition of covariance matrix, and Ng even says that SVD is numerically more stable than eigendecomposition.

From my understanding, for PCA we should do SVD of the data matrix of (m,n) size, not of the covariance matrix of (n,n) size. And eigenvector decomposition of covariance matrix.

Why do they do SVD of covariance matrix, not data matrix?