(adsbygoogle = window.adsbygoogle || []).push({}); Real Analysis: What does it mean for the set of invertible nxn matrices to be open?

1. The problem statement, all variables and given/known data

The set of invertible nxn matrices is open in M, is it also dense?

2. The attempt at a solution

Let S = set of invertible nxn matrics, S contained in M

Let A be any invertible element in S. We want to show that there exists an open ball of ivertible elements centered at A. Let 0 < d < det^-1(A)

But I have ho idea what it means for the set of invertible nxn matrices to be open or how to proceed from here. Any help would be great!

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# What what does it mean for the set of invertible nxn matrices to be open?

**Physics Forums | Science Articles, Homework Help, Discussion**