Re: Derivative wrt vector

If $\displaystyle a$, $\displaystyle \mu$, and $\displaystyle x$ are vectors, how are you defining "$\displaystyle ax$" and "$\displaystyle \mu x$"? Is that the dot product? But then it wouldn't make sense to take the norm of $\displaystyle ax- \mu x$ which would be a **number**! Are you sure that $\displaystyle a$ and $\displaystyle \mu$ are not **scalars**?

Re: Derivative wrt vector

yes, the dot product is meant here and the result of the term should be a number. I need to find the optimal value of x given a and mu.

Re: Derivative wrt vector

Quote:

Originally Posted by

**goftl** yes, the dot product is meant here and the result of the term should be a number. I need to find the optimal value of x given a and mu.

you can just combine a and $\mu$ into

$c=a-\mu$ and then find $x$ to minimize

$\dfrac {\|c\cdot x\|^2}{\|x\|^2}$

This is clearly minimized if $x$ is orthogonal to $c$

As $c\in \mathbb{R}^n$ there is an (n-1) dimensional subspace containing all these vectors orthogonal to $c$

Re: Derivative wrt vector

thanks this helped me a lot!