# Comparing condition numbers

I have two matrices, $$A$$ and $$B$$ where $$A,B \in R_{mxn}$$ ($$m>>n$$). I need to answer the question: Which one is better-conditioned among $$A$$ and $$B$$ ? However, I will be making these comparisons for tons of large matrices and therefore, I am reluctant to explicitly calculate condition numbers for all of them. Is there any way of making this comparison without a computationally expensive process?

• I suspect that you could get a reasonable estimate for the condition number by randomly sampling unit vectors; might be an approach to take. – Omnomnomnom Aug 20 at 20:47