Geometric interpretation of complex vectors arising in the frequency-domain analysis of multivariable systems

It is shown that an
n
-dimensional vector whose components are complex numbers can be visualized as a plane ellipse in geometric
n
-space. The length and direction of a complex vector are interpreted in terms of the ellipse axes thus giving a deeper insight into the eigenstructure of system transfer matrices. The system characteristic ellipse is introduced and its application to the measurement of characteristic loci is discussed.