I need to minimize

,

where x, a and are vectors in .

My Idea was to take the derivative, set it to zero and solve for x, but I'm not good in matrix calculus. I would be extremely thankful if somebody could help me here!

Printable View

- August 13th 2014, 05:56 AMgoftlDerivative wrt vector
I need to minimize

,

where x, a and are vectors in .

My Idea was to take the derivative, set it to zero and solve for x, but I'm not good in matrix calculus. I would be extremely thankful if somebody could help me here! - August 13th 2014, 06:23 AMHallsofIvyRe: Derivative wrt vector
If , , and are vectors, how are you defining " " and " "? Is that the dot product? But then it wouldn't make sense to take the norm of which would be a

**number**! Are you sure that and are not**scalars**? - August 13th 2014, 06:51 AMgoftlRe: 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.

- August 13th 2014, 08:59 AMromsekRe: Derivative wrt vector
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 $c$ - August 15th 2014, 03:50 AMgoftlRe: Derivative wrt vector
thanks this helped me a lot!