Engineering

The singular value decomposition, and how much of an order book is really there

SVD is the workhorse under PCA, factor models and a good deal of applied machine learning. What it actually computes, why it is the best low-rank approximation rather than merely a convenient one, what its factors look like on the NIFTY and SENSEX futures books, why the same procedure gives two answers that cannot be compared, and the random-matrix result that says most of what it finds in market data is noise.