  Irreducible bilinear tensorial concomitants of an arbitrary complex
antisymmetric valence-2 tensor are derived in four-dimensional spacetime. In
addition these bilinear concomitants are symmetric (or antisymmetric),
self-dual (or anti-self-dual), and hermitian forms in the antisymmetric tensor.
An important example of an antisymmetric valence-2 tensor, or bivector, is the
electromagnetic field strength tensor which ordinarily is taken to be
real-valued. In generalizing to complex-valued bivectors, the authors find the
hermitian form versions of the well-known electromagnetic scalar invariants and
stress-energy-momentum tensor, but also discover several novel tensors of total
valence 2 and 4. These tensors have algebraic similarities to the Riemann,
Weyl, and Ricci tensors.
