Question: Given a data matrix X in Rn dX in Rn d where dd is much smaller than nn and k = rank ( X )

Given a data matrix X in RndX in Rnd where dd is much smaller than nn and k=rank(X)k=rank(X), if we project our data onto a kk-dimensional subspace using PCA, our projection will have zero reconstruction error (in other words, we find a perfect representation of our data, with no information loss).

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