Solved – PCA iteratively finds directions of greatest variance; but how to find a whole subspace with greatest variance?

Principal component analysis (PCA) works like this: the first greatest variance on the first principal component, the second greatest variance on the second principal component, and so on.

For me there is a problem with this iterative process.

What if I know I only want two principal components in order to visualize my data in 2 dimensions?

The two first PCs are not the best because the second one is the best 2nd PC but with the 1st PC they don't constitute the best couple of principal components.

Is there a way to find the "best couple" of principal components, meaning two-dimensional subspace with the greatest variance?

The first two are the two best first two. The second one takes the first one into account.

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