---
title: "sparsity"
type: concept
related: [Lu Factorization]
source: https://www.jemoka.com/posts/kbhsparsity/
confidence: high
status: active
---

A bunch of matricies could be sparse; for fluid dynamics, for instance, has a \(10^{6} \times 10^{6}\) matrix, but may only have \(7 \times 10^{6}\) non-zero entries; but the inverse could be fully dense!
In these cases, we almost never want to form a in inverse if needed.
If we really need to invert this, performing a LU-Factorization is going to be a very good idea.
