1. ## what is n_2?

in one of my questions a 2x2 matrix is mentioned that is$\displaystyle \eta_{2}$, it doesnt tell me what it is but somewhere else in my notes it mentions that $\displaystyle det(\eta_{2})=-1$. can someone please tell me (quickly) what this matrix is?

2. ## Re: what is n_2?

Originally Posted by wik_chick88
in one of my questions a 2x2 matrix is mentioned that is$\displaystyle \eta_{2}$, it doesnt tell me what it is but somewhere else in my notes it mentions that $\displaystyle det(\eta_{2})=-1$. can someone please tell me (quickly) what this matrix is?
Haha, there are quite a few matrices with $\displaystyle \det(\eta_2)=-1$. Can you give us more context.

3. ## Re: what is n_2?

In general, a linear transformation with negative determinant changes orientation, but as Drexel28 comments, we need more context. For example if $\displaystyle A\in\mathbb{R}^{2\times 2}$ with $\displaystyle \det A=-1$ and $\displaystyle A$ orthogonal we have a symmetry with respect to a line.