  The topological equivalence classification for linear flows on $\mathbb{R}^n$
had been completely solved by Kuiper and independently Ladis in 1973. However,
Ladis' proof was published in a Russian journal which isn't easily available,
Kuiper's proof is more topological and a little bit subtle. Aiming at
topological conjugacy classification, mainly based on the ideas of Kuiper, we
introduce other techniques and try to present an elementary and self-contained
proof just using linear algebra and elementary topology.
