One of the OLS assumptions concerning the X-matrix (with a constant) is that the columns $(1, x_{i1}, · · · , x_{iK})$ are not linearly dependent. This looks intuitive to me, because of the dummy-variable trap.
In another text book I found the assumption is $E[x_i \cdot x_i']$ is positive definite and finite and that the rank(X) = K + 1.
Now I understand that X has to be a full rank matrix, because the column rank is equal to its row rank. So that is the same statement as in the first assumption. But how is "$E[x_i \cdot x_i']$ is positive definite and finite" related to that?
Thanks a lot!