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Thread: what is n_2?

  1. #1
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    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?
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  2. #2
    MHF Contributor Drexel28's Avatar
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    Re: what is n_2?

    Quote Originally Posted by wik_chick88 View Post
    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.
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  3. #3
    MHF Contributor FernandoRevilla's Avatar
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    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.
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