OLS with duplicate signals

A return model includes two identical feature columns. Are its ordinary least-squares coefficients and fitted values unique? Explain how you would fit it numerically.

The coefficient vector is not unique because the design matrix is rank deficient: a null-space vector can be added without changing the fit. The fitted vector is the unique orthogonal projection onto the column space. Use a QR/SVD least-squares solver or remove redundant columns. A pseudoinverse selects the minimum-norm coefficient vector; it does not make the original coefficients identifiable.