[LA] Orthogonal contrasts

Definition(one contrast): linear combination of group mean vectors $\Phi = \sum_{g=1}^G c_g \hat\mu_g$ is a contrast if $\sum_{g=1}^G c_g =0$
Definition(two contrasts): two contrasts $\Phi_1 = \sum_{g=1}^G c_g \hat\mu_g$ and $\Phi_2 = \sum_{g=1}^G d_g \hat\mu_g$ are orthogonal if $\sum_{g=1}^G \frac{c_g d_g}{n_g}=0$

application can be found in
http://blog.youkuaiyun.com/comeyan/article/details/50514596