Prove that kernel PCA is equivalent to applying standard PCA to the data transformed by the kernel by showing that solving the eigenvalue problem for the kernel matrix is equivalent to solving the...

Prove that kernel PCA is equivalent to applying standard PCA to the data transformed by the kernel by showing that solving the eigenvalue problem for the kernel matrix is equivalent to solving the eigenvalue problem for the covariance matrix in the feature space. Assume that the data in the feature space is centered.