What is this symbol called?

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Not much to this question, just can't find the name.

I cannot find what this symbol is called, its like a n with a tail before it. It is something to do with eigenvectors in my context.

Purpose is I need to put it in LaTeX.

weird n with a curve before it

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I assume you are refering to

$$\large\eta$$

which is the greek letter "eta".

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Actually, in your post it is $$ \hat{\eta}_A. $$ The greek letter is $\eta$.