Choice of Principal Components in PCA

For computing PCA of $X$, do we use the eigenvectors of covariance matrix $X^TX$, or the eigenvectors of kernel matrix $XX^T$ as the principal components?

I am really confused, because seen both used.

-

Basically, PCA is to find the vectors that can diagonalize the covariance matrix, so you need to find the eigenvectors of the covariance matrix, which are the principle components. In you case, the principle components are also the right singular vectors of the data matrix $X$ where each column corresponds to a random variable, so you can use the SVD to compute them.