Towards a geometrical interpretation of rainbow geometries

Towards a geometrical interpretation of quantum information compression

Let S be the von Neumann entropy of a finite ensemble E of pure quantum states. We show that S may be naturally viewed as a function of a set of geometrical volumes in Hilbert space defined by the states and that S is monotonically increasing in each of these variables. Since S is the Schumacher compression limit of E , this monotonicity property suggests a geometrical interpretation of the qua...

Geometrical Realizations of Shadow Geometries

Contents Introduction 615 General definitions and notation 618 § 1. Shadow geometries of incidence geometries 619 § 2. Shadow geometries of chamber systems and their geometrical reali-zations 626 § 3. Interpreting the shadow geometries as tessellations. .. . 6 3 1 § 4. Transitive tessellations for reflection groups 636 § 5. The Delaney symbols of the tessellations with a transitive reflection g...

A geometrical interpretation of the inverse matrix

A New Geometrical Interpretation of Trilinear Constraints

We give a new geometrical interpretation of the well-known algebraic trilinear constraints used in motion analysis from three views observation. We show that those algebraic equations correspond to depth errors appropriately weighted by a function of the relative reliability of the corresponding measurements. Therefore directly minimizing the algebraic trilinear equations, in the least squares ...

Geometrical Interpretation of Constrained Systems

The standard approach to classical dynamics is to form a Lagrangian which is a function of n generalized coordinates qi, n generalized velocities q̇i and parameter τ . The 2n variables qi, q̇i form the tangent bundle TQ. The passage from TQ to the cotangent bundle T ∗Q is achieved by introducing generalized momenta and a Hamiltonian. However, this procedure requires that the rank of Hessian matrix