Related papers: Linear projections and successive minima
This paper is devoted to presenting a new approach to determine the intersection of two quadrics based on the detailed analysis of its projection in the plane (the so called cutcurve) allowing to perform the corresponding lifting correctly.…
We study linear series on curves inducing injective morphisms to projective space, using zero-dimensional schemes and cohomological vanishings. Albeit projections of curves and their singularities are of central importance in algebraic…
For given real or complex $m \times n$ data matrices $X$, $Y$, we investigate when there is a matrix $A$ such that $AX = Y$, and $A$ is invertible, Hermitian, positive (semi)definite, unitary, an orthogonal projection, a reflection, complex…
A grid polygon is a polygon whose vertices are points of a grid. We define an injective map between permutations of length n and a subset of grid polygons on n vertices, which we call consecutive-minima polygons. By the kernel method, we…
In this short note we give incremental algorithms for the following lattice problems: finding a basis of a lattice, computing the successive minima, and determining the orthogonal decomposition. We prove an upper bound for the number of…
We provide a complete classification, in the language of weak-combinatorics, of minimal plus-one generated line arrangements in the complex projective plane with double and triple intersection points.
Many important values for cooperative games are known to arise from least square optimization problems. The present investigation develops an optimization framework to explain and clarify this phenomenon in a general setting. The main…
We give a precise mathematical formulation for the notions of a parametric patch and linear precision, and establish their elementary properties. We relate linear precision to the geometry of a particular linear projection, giving necessary…
Multivariate data is often visualized using linear projections, produced by techniques such as principal component analysis, linear discriminant analysis, and projection pursuit. A problem with projections is that they obscure low and high…
In this paper, we discuss the minimal surfaces over the slanted half-planes, vertical strips, and single slit whose slit lies on the negative real axis. The representation of these minimal surfaces and the corresponding harmonic mappings…
Given a web (multi-foliation) and a linear system on a projective surface we construct divisors cutting out the locus where some element of the linear system has abnormal contact with the leaf of the web. We apply these ideas to reobtain a…
Probabilistic ideas and tools have recently begun to permeate into several fields where they had traditionally not played a major role, including fields such as numerical linear algebra and optimization. One of the key ways in which these…
We discuss representations of the projective line over a ring $R$ with 1 in a projective space over some (not necessarily commutative) field $K$. Such a representation is based upon a $(K,R)$-bimodule $U$. The points of the projective line…
Extensions of previous linear regression models for interval data are presented. A more flexible simple linear model is formalized. The new model may express cross-relationships between mid-points and spreads of the interval data in a…
The projection lemma (often also referred to as the elimination lemma) is one of the most powerful and useful tools in the context of linear matrix inequalities for system analysis and control. In its traditional formulation, the projection…
We show how the recent improvement of the Hermite-Hadamard inequality can be applied to some (not necessarily convex) planar figures and three-dimensional bodies satisfying some kind of regularity.
The notion of symmetry in polynomial rings with several indeterminates is generalized to polynomial rings over finite fields. Families of extensions of the projective line over a finite field of constants possessing this property are…
The least square solution of minimum norm of a rectangular linear system of equations can be found out iteratively by using matrix splittings. However, the convergence of such an iteration scheme arising out of a matrix splitting is…
We investigate the use of linear programming tools for solving semidefinite programming relaxations of quadratically constrained quadratic problems. Classes of valid linear inequalities are presented, including sparse PSD cuts, and…
Random Projection is a foundational research topic that connects a bunch of machine learning algorithms under a similar mathematical basis. It is used to reduce the dimensionality of the dataset by projecting the data points efficiently to…