The polarization of a complex vector in higher dimensions

The use of trigonometric identities facilitates the determination of the polarization of a vector quantity in two dimensions, but becomes rapidly unwieldy in higher dimensions. Instead, the polarization can be obtained from simple algebraic considerations when the problem is viewed as an eigenvalue-eigenvector problem. The authors derive the formulas, show that, regardless of the dimension, the eigenvalue may assume at most only two values, and conclude that because of this fact, the polarization of a complex vector is a two-dimensional concept with no higher dimensional analog