= Equiangular direction in least angle regression
{title2=$u=X_A^{s}w,\quad w=\alpha G_A^{-1}1,\quad\alpha=(1^TG_A^{-1}1)^{-1/2}$}
With signed active <covariate> columns $X_A^s=(s_jx_j)_{j\in A}$ and their positive-definite <Gram matrix> $G_A=(X_A^s)^TX_A^s$, the displayed direction has unit <norm> and $(X_A^s)^Tu=\alpha1$. Thus it makes equal angles with unit-length signed active <covariates>, and movement along it reduces their signed residual correlations at the common rate $\alpha$. The <regression coefficient> direction is $d_A=\operatorname{diag}(s_A)w$, with inactive components zero.
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