The M(λ) Surface

Abstract

It is well known that if n = 1, that is if the dimension of the system is 2, then the function M(λ) lies on a circle or is merely a point. A cursory check of the M(λ) equation, or its representation as

$$M = C + {{R}_{1}}U{{R}_{2}} = C + \rho {{e}^{{i\theta }}},$$

easily shows this to be true. In higher derivations, however, the surface is so complicated that it is impossible to visualize in any real sense. For example, if n = 4, the M(λ) function is a 2 × 2 complex matrix. It involves four complex components, and is too much for us in our three-dimensional world.