How can I geometrically represent condition number of an m by n matrix in 2D

Hi, I have a 5 by 20 matrix and I computed the condition number using MATLAB command: cond(A,2). But I would like a geometric view in 2D of how the matrix transform a unit circle into an ellipsoid like shown in the image.

Thanks

[Matt J]

But your matrix is a mapping from R^20 to R^5, not from R^2 to R^2. Is there a particular two dimensional sub-space that you are interested in?

[Ayinde]

I only want to know how the matrix stretches or distort a unit circle to depict how badly conditioned/scaled it is, that's why I am thinking of projecting it in 2D sub-space

[Matt J]

Projecting it onto which 2D sub-space? There are many in R^5 and even more in R^20

[Ayinde]

Thanks Matt J. I really don't know much about this projection onto subspace, but if I get clearly what you are trying to say, it means,say in R^5 space, one can choose any combination of two rows to project and same thing goes with R^20 where one can choose any combination of two columns. Am I right?

[Matt J]

That's true, but there are further possible 2D subspaces beyond those. Imagine for a moment that your A matrix is just A=eye(3). In this case, every 2D plane through the origin in R^3 is a possible subspace. There are uncountably infinite 2D subspaces.