Determinantal Systems of Points.

Sparse Systems of Parameters for Determinantal Varieties

Solving determinantal systems using homotopy techniques

Let K be a field of characteristic zero and K be an algebraic closure of K. Consider a sequence of polynomials G = (g1, . . . , gs) in K[X1, . . . , Xn], a polynomial matrix F = [fi,j ] ∈ K[X1, . . . , Xn], with p ≤ q, and the algebraic set Vp(F,G) of points in K at which all polynomials in G and all p-minors of F vanish. Such polynomial systems appear naturally in e.g. polynomial optimization,...

The determinantal method for Hill systems

where G ∈ L∞(IR, IRn×n) is a matrix valued function with G(x+1) = G(x) for almost every x ∈ IR. Systems of this type appear, for instance, in the theory of vibrations or in hydrodynamics. In the typical case where the function G depends on some set of parameters, one is not really interested in the solution of (1) but in the values of the parameters for which this equation is stable. Let Y : IR...

Linear systems and determinantal random point fields

Abstract Tracy and Widom showed that fundamentally important kernels in random matrix theory arise from systems of differential equations with rational coefficients. More generally, this paper considers symmetric Hamiltonian systems and determines the properties of kernels that arise from them. The inverse spectral problem for self-adjoint Hankel operators gives sufficient conditions for a self...

Roots of Bivariate Polynomial Systems via Determinantal Representations