matrix - Is "$\mathrm E[X'X]$ has rank $k$" the assumption of no multicollinearity?

My lecturer wrote this on the board: Assume $\mathrm E[X'X]=Q$ has rank $k$, where $X$ is the data matrix and $k$ is the number of independent variables.I asked her if that is the assumption of no multicollinearity, and she said, "No."I said that if one of the variables are a linear combination of the others, the rank will be less than $k$.She responded that the rank will still be $k$ if there is collinearity.Who is right?...Read more