Outer and Eigen: Tangent Concepts

In this paper we use the power of the outer exponential ${\mathrm{\Lambda }}^B$ of a bivector $B$ to see the so-called invariant decomposition from a different perspective. This is deeply connected with the eigenvalues for the adjoint action of $B$, a fact that allows a version of the Cayley-Hamilton theorem which factorises the classical theorem (both the matrix version and the geometric algebra version).