Given a space $ A \subset R^n$ , it follows that the $ l_2$ projections of the standard normal basis of $ R^n$ into $ A$ span $ A$ . Does this also hold if we use the $ l_1$ projection instead?
$ l_1$ denotes the taxicab norm while $ l_2$ denotes the euclidean norm.
A proof, counterexample, or even just an answer would be very appreciated. I’m studying sphere packing and as a consequence am trying to better understand the $ l_1$ norm.
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