  Given a subspace L of a vector space V, the Kalman variety consists of all
matrices of V that have a nonzero eigenvector in L. Ottaviani and Sturmfels
described minimal equations in the case that dim L = 2 and conjectured minimal
equations for dim L = 3. We prove their conjecture and describe the minimal
free resolution in the case that dim L = 2, as well as some related results.
The main tool is an exact sequence which involves the coordinate rings of these
Kalman varieties and the normalizations of some related varieties. We
conjecture that this exact sequence exists for all values of dim L.
