affine space


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affine space

[ə′fīn ‚spās]
(mathematics)
An n-dimensional vector space which has an affine connection defined on it.
References in periodicals archive ?
Another perspective, which may be more natural to some readers, is to consider the affine space {x' + N(A)} consisting of solutions to Az = b, where, x' is the solution of minimal norm.
n]]) by [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] and call it the n-dimensional affine space over [F.
Embeddings of Stein manifolds of dimension n into the affine space of dimension 3n/2 + 1.
The 21 papers propose an algorithm for continuous piecewise affine maps of compact support, investigate the stability of cycles in gene networks with variable feedbacks, and describe polynomial maps of the affine space.
Consequently the simultaneous rotations by equal intrinsic angle [phi][psi] of the intrinsic affine space coordinates of the symmetry-partner particles' frames [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] and -[phi][[?
794], is an affine space from which some parallel classes have been removed.
that contains the one-dimensional intrinsic rest mass pm0 of the particle in the intrinsic affine space coordinate [phi][?
One aspect that we stress more explicitly than Sonneveld and van Gijzen is that IDR(s) is a Krylov space method, and therefore the residuals lie in an affine space that is embedded in a Krylov subspace.
In other words, our considerations take place in an arbitrary affine space.
The extended three-dimensional affine space constituted by the affine coordinates [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] cannot hold matter (or mass of particles and objects).
It is quite obvious for a mathematician that the authors confuse a vector space with an affine space.
focuses on theory as he explains affine spaces and connections, Hessian structures, including their relations with Kahlerian and Codazzi structures, curvatures for Hessian structures, regular convex cones, Hessian structures and affine differential geometry, Hessian structures and information geometry, the cohomology of flat manifolds, compact Hessian manifolds, symmetric spaces with invariant Hessian structures, homogeneous spaces with invariant Hessian structures, and homogeneous spaces with invariant projectively flat connections.