the.com/sparse matrix
a grid that's almost entirely empty, and proud of it.
means a matrix where most entries are zero, so you store only the nonzero ones and save massive amounts of memory and compute.
from emerged from 1960s numerical computing, when engineers solving huge systems of equations realized storing every zero in a million-by-million matrix was insane, so formats like coordinate lists and compressed rows were born to skip them.
storage trickstores only value, row, column triples
csr formatcompressed sparse row cuts memory drastically
graphs love itadjacency matrices are almost always sparse
thresholdoften under 1 percent entries nonzero
for instance
google pagerank matrix — billions of pages, each linking to only a handful
recommender systems — netflix matrix of users times movies, mostly unrated
finite element solvers — engineering simulations with millions of near-empty equations
scipy sparse module — csr_matrix and csc_matrix used across scientific python