In the following equation $Av = \lambda v$ $v$ cannot be $\vec{0}$

Question

In this question and answers to such question people say that $v$ cannot be $\vec{0}$, but this not correct in my opinion. We assume it is different from $\vec{0}$ because otherwise $Av = \lambda v$ would be trivially true, right?

So, instead of saying "but this is a contradiction because $v$ cannot be $\vec{0}$" we should say "but this is a contradiction because, by assumption, $v \neq \vec{0}$", right?

I just wanted to clarify this point.

Answer 1

As it states already in the question, thats the contradiction...

(sorry cant comment as of yet)