What is the metric used here?

Question

Suppose we consider a set of all $n\times n$ matrices and if we consider them as metric space what is the metric we are using?

Is that determinant the metric we are following or is there any metric (other than discrete metric)

( I'm working on the problem : is $GL(n,\mathbb R)$ dense in $M(n,\mathbb R)$

score 2 · Answer 1 · answered Sep 02 '18 at 16:08

2

Since the set of square matrices of size $n$ is finite-dimensional, it does not matter: all norms are equivalent, they induce the same topology.

By the way, there is a ambiguity in your question, the title says norm and the core of the question metric, the claim above is false for metrics.

answered Sep 02 '18 at 16:08

C. Falcon

I'm sorry ! i'm interested in metrics ,I think norm also a metric .its my fault ,I will correct it, thanks! – Cloud JR K Sep 02 '18 at 16:12
1

You should tell us more about the context of the problem you are working on, it will help us guessing what is the metric used. – C. Falcon Sep 02 '18 at 16:15
I added it !... – Cloud JR K Sep 02 '18 at 16:16

1 Answers1