 Hotelling test of linear hypotheses

For a fixed rank-$m$ constraint matrix $B$, apply Hotelling's T-squared statistic to the transformed observations $B{X}_j$. Under $B\mu =0$, $(n-m)T_B^2/(m(n-1))\sim F_{m,n-m}$ for $n>m$. If the displayed contrasts are dependent, use a basis of their row space and replace $m$ by the rank.