Projective space

Projective space

Projective space is a mathematical concept that exists in a higher dimension than Euclidean space and includes additional points known as "points at infinity." Geometric transformations can be applied to move these points to traditional points and vice versa. Each family of parallel lines in the affine plane corresponds to a point at infinity in projective space, where they all intersect.From: Mechanical and Physico-Chemical Characteristics of Modified Materials [2019], Computer Graphics [2019]

Geometry

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Published in Leslie Hogben, Richard Brualdi, Anne Greenbaum, Roy Mathias, Handbook of Linear Algebra, 2006

Mark Hunacek

If V is an (n + 1)-dimensional vector space over a field F, then the n-dimensional projective space based onV, denoted P(V), is the set of all subspaces of V. The one-dimensional subspaces of V are the points of P(V); the two-dimensional subspaces of V are the lines of P(V). More generally, the k-dimensional projective subspaces are the (k + 1)-dimensional subspaces of V.

Typical Applications for Computer Vision

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Published in Ravi Das, Practical AI for Cybersecurity, 2021

Ravi Das

If these 2-Dimensional Points make use of what are known as “Heterogenous Coordinates,” these can then be implemented back into their geometric plane, which is technically known as a “2-Dimensional Projective Space.” Various kinds of Homogenous Vectors are thus used, and they be mathematically represented as follows: X = (X, Y, W) = W(X, y, 1) = WXi

A review on some classes of algebraic systems

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Journal Information

Published in International Journal of Control, 2020

Víctor Ayala, Heriberto Román-Flores

The solutions of the projected system (3) are denoted by for the initial value . The real projective space is determined by a quotient manifold , where the antipodal differentiable equivalence relation is defined by .

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Geometry

Typical Applications for Computer Vision

A review on some classes of algebraic systems