Related papers: The complement of a point subset in a projective s…

We consider the method of alternating projections for finding a point in the intersection of two closed sets, possibly nonconvex. Assuming only the standard transversality condition (or a weaker version thereof), we prove local linear…

For an axiomatization of three-dimensional projective space based on points and planes, we discuss appropriate versions of the harmonicity axiom and the projectivity axiom, showing that each axiom is equivalent to its spatial dual.

We investigate connections between the geometry of linear subspaces and the convergence of the alternating projection method for linear projections. The aim of this article is twofold: in the first part, we show that even in Euclidean…

We found strong similarities between the gravitational lensing and the conventional optical lensing. The similarities imply a graded refractive index description of the light deflection in gravitational field. We got a general approach to…

We consider the isoperimetric problem for the sum of two Gaussian densities in the line and the plane. We prove that the double Gaussian isoperimetric regions in the line are rays and that if the double Gaussian isoperimetric regions in the…

We consider the metric transformation of metric measure spaces/pyramids. We clarify the conditions to obtain the convergence of the sequence of transformed spaces from that of the original sequence, and, conversely, to obtain the…

We study the complement problem in projective spaces $\mathbb{P}^n$ over any algebraically closed field: If $H, H' \subseteq \mathbb{P}^n$ are irreducible hypersurfaces of degree $d$ such that the complements $\mathbb{P}^n \setminus H$,…

We determine those maps between affine or projective spaces that are linear in the abstract sense of transforming collinear points into collinear points and whose restriction to any line is constant or injective. Our results are extensions…

An introductory overview of vector spaces, algebras, and linear geometries over an arbitrary commutative field is given. Quotient spaces are emphasized and used in constructing the exterior and the symmetric algebras of a vector space.…

Any set of $\sigma$-Hermitian matrices of size $n \times n$ over a field with involution $\sigma$ gives rise to a projective line in the sense of ring geometry and a projective space in the sense of matrix geometry. It is shown that the two…

An embedding of a point-line geometry \Gamma is usually defined as an injective mapping \epsilon from the point-set of \Gamma to the set of points of a projective space such that \epsilon(l) is a projective line for every line l of \Gamma,…

Botelho, Jamison, and Moln\'ar \cite{BJM}, and Geh\' er and \v{S}emrl \cite{GeS} have recently described the general form of surjective isometries of Grassmann spaces of all projections of a fixed finite rank on a Hilbert space $H$. As a…

In our previous work, we provided an algebraic proof of the Zinger's comparison formula between genus one Gromov-Witten invariants and reduced invariants when the target space is a complete intersection of dimension two or three in a…

We compute the elementary divisors of the adjacency and Laplacian matrices of the Grassmann graph on $2$-dimensional subspaces in a finite vector space. We also compute the corresponding invariants of the complementary graphs.

We show that the pair given by the power set and by the "Grassmannian"(set of all subgroups) of an arbitrary group behaves very much like the pair given by a projective space and its dual projective space. More precisely, we generalize…

Given $2n$ points in the plane, it is well-known that there always exists a perfect straight-line non-crossing matching. We show that it is $NP$-complete to decide if a partial matching can be augmented to a perfect one, via a reduction…

This paper describes a numerical method for finding good packings in Grassmannian manifolds equipped with various metrics. This investigation also encompasses packing in projective spaces. In each case, producing a good packing is…

We propose a generalization of the classical point-line Cremona-Richmond configuration to a configuration of points and more dimensional subspaces of a projective space, and present them as geometric realizations of some interesting…

Using the concept of projective systems for linear codes and elementary linear algebra, we show that projective $[n,k]_q$ codes form a connected subgraph in the Grassmann graph consisting of $k$-dimensional subspaces of an $n$-dimensional…

The method of alternating projections involves orthogonally projecting an element of a Hilbert space onto a collection of closed subspaces. It is known that the resulting sequence always converges in norm if the projections are taken…