I am studying about multicollinearity in regression and in the book it says, "if there is severe (but not perfect) multicollinearity, two or more predictor variables are highly correlated, so $X^TX$ is (computationally) difficult to invert. This produces unstable regression estimates and large standard error.
Could anyone explain me, what makes it computationally difficult? Any mathematical explanation of the fact would be really helpful.
some of the rows/columns in the covariance matrix are (very closely) linearly dependent which makes the matrix hard to invert. Small numerical errors may cause significant changes in the inverted matrix output