I have a vector $v = a_1\mu_1 + a_2\mu_2 + ... + a_n\mu_n$ where $\mu_i$ are given linearly independent but not orthogonal vectors.
I need to choose $k$ vectors from the original set such that when I project $v$ onto the space spanned by these vectors, the length of the projection is highest possible.
Are there any algorithms that could solve this problem? $n$ is very large number.