Consider the problem for some vectors $v,m\in {\mathbb{R}}^{n}:$

$f(v)=({v}^{T}m{)}^{2}$

w.r.t $\Vert v{\Vert}^{2}=1$

I want to maximize f

If I consider the lagrangian, I get:

$L(v)=({v}^{T}m{)}^{2}+\lambda (1-\Vert v{\Vert}^{2})$

Taking derivative, I get: $2m{m}^{T}v-\lambda 2v=0$ Therefore $m{m}^{T}v=\lambda v(\ast )$

Multiplying by ${v}^{T}$ from left, I end up with

$({v}^{T}m{)}^{2}=\lambda $

If I put that in(*), I do cannot simplfy that.

Is there a trick I can apply?

$f(v)=({v}^{T}m{)}^{2}$

w.r.t $\Vert v{\Vert}^{2}=1$

I want to maximize f

If I consider the lagrangian, I get:

$L(v)=({v}^{T}m{)}^{2}+\lambda (1-\Vert v{\Vert}^{2})$

Taking derivative, I get: $2m{m}^{T}v-\lambda 2v=0$ Therefore $m{m}^{T}v=\lambda v(\ast )$

Multiplying by ${v}^{T}$ from left, I end up with

$({v}^{T}m{)}^{2}=\lambda $

If I put that in(*), I do cannot simplfy that.

Is there a trick I can apply?