# Conjugate Gradient, initial direction set to initial residual

In the (iterative) Conjugate Gradient (CG) algorithm: https://en.wikipedia.org/wiki/Conjugate_gradient_method

The initial search direction $p_{0}$ is set to the initial residual $r_{0}$. But I can't see why this choice? Can I get this choice of $p_{0}$ from any of the equations presented in the article?

Thanks!

Consider the equation $\mathbf{p}_k=\mathbf{r}_k-\sum_{i<k} \frac{\mathbf{p}_i^T\mathbf{A}\mathbf{r}_k}{\mathbf{p}_i^T\mathbf{A}\mathbf{p}_i}\mathbf{p}_i$ for $k=0$. Equivalently, and in terms of what's actually going on, we are correcting the search direction of steepest descent to be $\mathbf{A}$ orthogonal to the previous search directions. For the first step we have no other search directions and just look along the residual directly.