I am not a native speaker of English but reading "Introduction to Machine Learning".
Chapter 5. Multivariate Methods has a sentence in which an intransitive verb "correct" occurs but I can't pinpoint its intended meaning.
"In the expanded Mahalanobis distance of equation 5.11, each variable is normalized to have unit variance, and there is the cross-term that corrects for the correlation between the two variables."
Do you have some intuitive paraphrases for "correct for"?
It means the same thing as "compensates for the error induced by"
In your example, if you leave off the cross term, your equation is incorrect because it doesn't take into account the correlation between the two variables. When you add in the cross term (presumably a function of the covariance) this error is compensated for.
This would be a correct (but unusual) use of the term in lay English as well.