Related papers: Some comments about measures, Jacobians and Moore-…
In the last decades the Moore-Penrose pseudoinverse has found a wide range of applications in many areas of Science and became a useful tool for physicists dealing, for instance, with optimization problems, with data analysis, with the…
We establish an invertibility criterion for free polynomials and free functions evaluated on some tuples of matrices. We show that if the derivative is nonsingular on some domain closed with respect to direct sums and similarity, the…
An effective numerical method is presented for optimizing model parameters that can be applied to any type of system of non-linear equations and any number of data-points, which does not require explicit formulation of the objective…
Motivated by recent results in random matrix theory we will study the distributions arising from products of complex Gaussian random matrices and truncations of Haar distributed unitary matrices. We introduce an appropriately general class…
We develop a probabilistic approach to the celebrated Jacobian conjecture, which states that any Keller map (i.e. any polynomial mapping $F\colon \mathbb{C}^n \to \mathbb{C}^n$ whose Jacobian determinant is a nonzero constant) has a…
A new generalized matrix inverse is derived which is consistent with respect to arbitrary nonsingular diagonal transformations, e.g., it preserves units associated with variables under state space transformations, thus providing a general…
We develop the first stochastic incremental method for calculating the Moore-Penrose pseudoinverse of a real matrix. By leveraging three alternative characterizations of pseudoinverse matrices, we design three methods for calculating the…
We present here the necessary and sufficient conditions for the invertibility of tridiagonal matrices, commonly named Jacobi matrices, and explicitly compute their inverse. The techniques we use are related with the solution of…
We consider the inverse dynamic problem for a dynamical system with discrete time associated with a semi-infinite complex Jacobi matrix. We propose two approaches of recovering coefficients from dynamic response operator and answer a…
Solving complex optimization problems in engineering and the physical sciences requires repetitive computation of multi-dimensional function derivatives. Commonly, this requires computationally-demanding numerical differentiation such as…
We consider matrix orthogonal polynomials related to Jacobi type matrices of weights that can be defined in terms of a given matrix Pearson equation. Stating a Riemann-Hilbert problem we can derive first and second order differential…
Multi-wave inverse problems are indirect imaging methods using the interaction of two different imaging modalities. One brings spatial accuracy, and the other contrast sensitivity. The inversion method typically involve two steps. The first…
We generalize the Wedderburn rank reduction formula by replacing the inverse with the Moore--Penrose pseudoinverse. In particular, this allows one to remove the non--singularity of a certain matrix from assumptions. The results implies in a…
One develops {\em ab initio} the theory of rational/birational maps over reduced, but not necessarily irreducible, projective varieties in arbitrary characteristic. A numerical invariant of a rational map is introduced, called the Jacobian…
The notion of the Moore-Penrose inverse of tensors with the Einstein product was introduced, very recently. In this paper, we further elaborate this theory by producing a few characterizations of different generalized inverses of tensors. A…
In this paper, we introduce new representation and characterization of the weighted core inverse of matrices. Several properties of these inverses and their interconnections with other generalized inverses are also explored. Through…
We discuss various factorial properties of subrings as well as properties involving irreducible and square-free elements, in particular ones connected with Jacobian conditions.
We study the proportion of metric matroids whose Jacobians have nontrivial $p$-torsion. We establish a correspondence between these Jacobians and the $\mathbb{F}_p$-rational points on configuration hypersurfaces, thereby relating their…
We prove that a polynomial map is invertible if and only if some associated differential ring homomorphism is bijective. To this end, we use a theorem of Crespo and Hajto linking the invertibility of polynomial maps with Picard-Vessiot…
Some inverse problems for semi-infinite periodic generalized Jacobi matrices are considered. In particular, a generalization of the Abel criterion is presented. The approach is based on the fact that the solvability of the Pell-Abel…