Note that LDA likely does not give the optimal separating hyperplane when minimizing out-of-sample error. That honor likely belongs to SVMs, and in practice tweaking the kernel and identifying relevant non-linear relationships generally become more important to finding a reasonable classification boundary.
Just a note that LDA is also used as a common acronym for Latent Dirichlet Allocation: <a href="http://en.wikipedia.org/wiki/Latent_Dirichlet_allocation" rel="nofollow">http://en.wikipedia.org/wiki/Latent_Dirichlet_allocation</a>