B4. Some Derivatives of Scalar Value Functions With Respect to a Vector

The first derivative of the scalar product of two Vectors $\vec{a}$ and $\vec{p}$ is

$$\frac{\partial \vec{a} \vec{p}} {\partial \vec{p}} = \frac{\partial \vec{p} \vec{a}} {\partial \vec{p}} = \vec{a}$$ (B6)

if vector $\vec{a}$ is independent of $\vec{p}$.

The derivative of the matrix built by the product of $\vec{p}^{\cal T} \mathcal{A} \vec{p}$ is

$$\frac{\partial \vec{p}^{\cal T} \mathcal{A} \vec{p}} {\part... ...} = \left ( \mathcal{A} + \mathcal{A}^{\cal T} \right) \vec{p}$$ (B7)

if the matrix $\mathcal{A}$ is quadratic and independent of $\vec{p}$.