Singular matrices using inv

Hi,

I have thousands of matrices that I would like to invert. I am interested in the resulting inverse matrices (they are biologically meaningful) so part of my script records each inverse. A small number of these matrices are badly scaled and a warning message appears

(Warning: Matrix is close to singular or badly scaled. Results may be inaccurate. RCOND = 1.554242e-018).

I have many matrices and can afford to not record 'unreliable' inverses.

I have two questions: 1. What is the rcond tolerance used in the inv function that flags the warning? (I can use this to prevent my code recording these inverses)

2. If no warning is flagged does this mean that the inverses are OK or should I go for something stricter (e.g. log(Condition number)< the precision of matrix entries)?

I hope this makes sense, any help would be greatly appreciated!