Singular matrix E in LSQ subproblem

The LSQ subproblem involves finding a solution to a linear system of equations where the matrix of coefficients is not necessarily square. If the matrix, denoted E, is singular (i.e., it has no inverse), then there may be no unique solution to the system.

In this case, additional constraints or assumptions may need to be imposed on the problem in order to obtain a unique solution. This can include adding regularization terms to the objective function or using techniques such as singular value decomposition (SVD) to obtain a pseudo-inverse of the matrix.