Given a large amount of data, how would I determine the degree of collinearity between all the variables? Preferably without relying on calculating linear regression between a variable and every other variable? Specifically, I need to find the collinearity between any single variable and every single other variable.

For this instance, we'll say the data has 10k variables and 100 million lines. I don't need a software package per se, a link to a relevant paper is fine.