The projections of a vector Ax along a certain orthonormal basis are chosen as the n components of a vector ρ. As the vector x sweeps the n–dimensional space, the locus of the point vector ρ is a closed surface, called the ρ locus. Some of the properties of the ρ locus are similar to those of the eigenvalues of the A matrix. These properties are exploited in the analysis of the unforced, linear time-invariant, dynamical system given by ẋ = Ax and for the forced systems of the ẋ = Ax + Bu, where u represents an impulse, step, ramp or sinusoidal input.