Using the Chern classes defined by Grothendieck, we map a K-theoretic invariant of invertible symmetric matrices defined by Giffen to the Clifford invariant.

Matrix population models are increasingly used in both theoretical and applied analysis of population dynamics (Caswell, Matrix Population Models*/Construction, Analysis, and Interpretation (2001) 722). The projected asymptotic growth rate from deterministic models, based on a single matrix, is invariant as to when in the annual cycle the population is censused (typically, either immediately pr...

Given the set of square matrices M ⊂ Mn+m(C) that keep the subspace W = Cnx{0} ⊂ C invariant, we obtain the implicit form of a miniversal deformation of a matrix a ∈ M, and we compute it explicitely when this matrix is marked (this is, if there is a permutation matrix p ∈ Mn+m(C) such that p−1ap is a Jordan matrix). We derive some applications to tackle the classical Carlson problem.

For two positive integers m and n, we let Hn be the Siegel upper half plane of degree n and let C be the set of all m × n complex matrices. In this article, we investigate differential operators on the Siegel-Jacobi space Hn ×C(m,n) that are invariant under the natural action of the Jacobi group Sp(n,R)⋉ H (n,m) R on Hn × C, where H R denotes the Heisenberg group.

Abstract: We obtain explicitly the renormalization group equations for the quark mass matrices in terms of a set of rephasing invariant parameters. For a range of assumed high energy values for the mass ratios and mixing parameters, they are found to evolve rapidly and develop hierarchies as the energy scale decreases. To achieve the experimentally observed high degree of hierarchy, however, th...

Let ‖ · ‖ be a unitary similarity invariant norm on the set Mn of n× n complex matrices. A description is obtained for surjective maps φ on Mn satisfying ‖AB− BA‖ = ‖φ(A)φ(B)−φ(B)φ(A)‖ for all A,B ∈ Mn . The general theorem covers the special cases when the norm is one of the Schatten p -norms, the Ky-Fan k -norms, or the k -numerical radii. Mathematics subject classification (2000): Primary 15...

In this paper, asymmetric Algebraic Riccati Equations are analyzed. We derive a new parametrization of the set of solutions, which may be viewed as alternative to the classical one based on Lagrangian subspaces of a “pseudo-Hamiltonian” matrix. Generalizing the symmetric case, the proposed parametrization is given in terms of pairs of invariant subspaces of two related “feedback” matrices. Exte...

We consider ecological difference equations of the form X i t+1 = X i t Ai(Xt) where X i t is a vector of densities corresponding to the subpopulations of species i (e.g. subpopulations of different ages or living in different patches), Xt = (X 1 t , X 2 t ,. .. , X m t) is state of the entire community, and Ai(Xt) are matrices determining the update rule for species i. These equations are perm...