The algebraic theory of latent projectors in lambda matrices

摘要

Multivariable systems and controls are often formulated in terms of differential equations, which give rise to lambda matrices of the form A(λ) = A0λn + A1λn-1 + ⋯ + An. The inverses of regular lambda matrices can be represented by the latent projectors or matrix residues that have very specific properties. This paper describes the general theory of latent roots, latent vectors, and latent projectors and gives the relationships to eigenvalues, eigenvectors, and eigenprojectors of the companion form.