structural:scholar_edition, information:highlighting, quality:corruption, quality:correction
Area-preserving flow

When tr A = 0 {\displaystyle \operatorname {tr} A=0}, we have det e A t = e tr (A) t = 1 {\displaystyle \det e^{At}=e^{\operatorname {tr} (A)t}=1}, so the flow is area-preserving. In this case, the type of flow is classified by det A {\displaystyle \det A}.