Let v be the column vector [1-i ; -3 ; -2i ; 0] and suppose v is an eigenvector of a Hermitian matrix M with eigenvalue -3. Calculate v^H M

What I did-

We know by definition Mv = -3v

Now, M = M^H because M is Hermitian. Then,

M^Hv = (v^H M)^H = conj(v^H M).

So, v^H M = conj(-3v)

Thoughts?

Thanks!