I'm wondering if it's possible to calculate in a percentage how symmetric a matrix is. So f.e. even if a matrix is not symmetrical, instead of just classifying it as "not symmetric" say that it's "symmetric with 80%".

My overall goal is to get kind of a "symmetry value" adding up values from different kind of symmetry like translational, rotational, etc.

  I appreciate any help :)

Thanks!

Is it possible to calculate a percentage that quantifies how symmetric a given matrix is?

For example, even if a given matrix is not symmetric, instead of just classifying it as "not symmetric", one can say that it's "$80\%$ symmetric".

My overall goal is to get a kind of a "symmetry score" adding up values of different kinds of symmetry (e.g., translational, rotational). I appreciate any help. Thanks!