Consider a linear programming model in the usual form ready for applying the simplex method. I understand that having the constraint equations' coefficient matrix $A$ be of full row rank means not having any redundancy in the constraints.
However, will $A$ not being of full row rank cause any problems in the application of the simplex algorithm? For example, if there is a degenerate basic feasible point that has not been preprocessed away, then the simplex algorithm (if unmodified) may go into an infinite loop and never terminate. How about when $A$ is not of full row rank?