Kennaugh＇s pseudo-eigenvalue equation is a basic equation that plays an extremely important role in radar polarimetry. In this paper, by means of real representation, we first present a necessary and sufficient condition for the general Kennaugh＇s pseudo-eigenvalue equation having a solution, characterize the explicit form of the solution, and then study the solution of Kennaugh＇s pseudo-eigenvalue equation. At last, we propose a new technique for finding the coneigenvalues and coneigenvectors of a complex matrix under appropriate conditions in radar polarimetry.
Let gl,,（R） be the general linear Lie algebra of all n×n matrices over a unital commutative ring R with 2 invertible, dn（R） be the Cartan subalgebra of gln（R） of all diagonal matrices. The maximal subalgebras of gln（R） that contain dn（F：） are classified completely.
