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B4. Some Derivatives of Scalar Value Functions With Respect to a Vector
The first derivative of the scalar product of two Vectors
and
is
![\begin{displaymath}
\frac{\partial \vec{a} \vec{p}}
{\partial \vec{p}} =
\frac{\partial \vec{p} \vec{a}}
{\partial \vec{p}} = \vec{a}
\end{displaymath}](img286.gif) |
(B6) |
if vector
is independent of
.
The derivative of the matrix built by the product of
is
![\begin{displaymath}
\frac{\partial \vec{p}^{\cal T} \mathcal{A} \vec{p}}
{\part...
...} =
\left ( \mathcal{A} + \mathcal{A}^{\cal T} \right) \vec{p}
\end{displaymath}](img288.gif) |
(B7) |
if the matrix
is quadratic and independent of
.
R. Plasun