Question

Are there multiple solutions to eigendecomposition of a covariance matrix or do all methods result in the same answer?

For principal components analysis, I need to find the largest k eigenvalues and associated eigenvectors, but there are many different algorithms for eigendecomposition.

Do they all result in the same answer at the end of the day, or are there some answers better than others?

Answer 1

Are there multiple solutions to eigendecomposition of a covariance matrix or do all methods result in the same answer?

A covariance matrix is a real positive definite matrix so if the eigenvalues are distinct then all eigendecomposition methods will output the same matrices, up to the signs of the eigenvectors. If you are doing PCA then you probably want to decompose the centered covariance matrix and not the covariance matrix itself.

Also your question is a newby question so we will probably be berated and closed. I think there's a statistics stackexchange that you could try if this happens.