In statistics, the SVD can be used to assess the conditioning of a design matrix, and thus the stability of the parameter coefficient estimates. One key advantage of this approach over the more common Variance Inflation Factors (VIF) is that it also allows detecting collinearity with the intercept column. One disadvantage is that it is much harder to explain to a nontechnical audience.

More information can be found here:

• Belsley, David A.; Kuh, E.; Welsch, R. E. Regression Diagnostics: Identifying Influential Data and Sources of Collinearity (Wiley, 1980)
• Belsley, David A. Conditioning Diagnostics: Collinearity and Weak Data in Regression (Wiley, 1991)
• Belsley, David A. (1991). A Guide to using the collinearity diagnostics. Computer Science in Economics and Management 4, 33-50