= Conjugate direction
{title2=$p_i^TAp_j=0\quad(i\ne j)$}
= A-conjugate direction
{c}
{synonym}
Nonzero <vectors> are conjugate directions with respect to a <symmetric positive-definite matrix> $A$ when they are pairwise <orthogonal> in the <inner product> $\langle u,v\rangle_A=u^TAv$. They need not be <orthogonal> in the ordinary Euclidean <inner product>. They are <linearly independent>: multiplying a vanishing <linear combination> by $p_j^TA$ isolates its $j$th coefficient times $p_j^TAp_j>0$.
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