Like... most of it? You can't do linear algebra "safely" without doing error analysis. So lots of decompositions and operations are very useful for proofs and f

Like... most of it? You can't do linear algebra "safely" without doing error analysis. So lots of decompositions and operations are very useful for proofs and finding bounds - but can't be use directly to compute values. It's why a good fraction of stuff people do with linear algebra is numerically garbage