  The first author with B. Sturmfels studied the variety of matrices with
eigenvectors in a given linear subspace, called Kalman variety. We extend that
study from matrices to symmetric tensors, proving in the tensor setting the
irreducibility of the Kalman variety and computing its codimension and degree.
Furthermore we consider the Kalman variety of tensors having singular t-ples
with the first component in a given linear subspace and we prove analogous
results, which are new even in the case of matrices. Main techniques come from
Algebraic Geometry, using Chern classes for enumerative computations.
