In-place matrix transposition: Difference between revisions

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A '''partial linear space''' (also '''semilinear''' or '''near-linear''' space) is a basic [[incidence structure]] in the field of incidence geometry, that carries slightly less structure than a [[linear space (geometry)|linear space]].
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==Definition==
Let <math>S=({\mathcal P},{\mathcal B}, \textbf{I}) </math> an incidence structure, for which the elements of <math>{\mathcal P}</math> are called ''points'' and the elements of <math>{\mathcal B}</math> are called ''lines''. ''S'' is a partial linear space, if the following axioms hold:
* any line is at least incident with two points
* any pair of distinct points is incident with at most one line
 
==References==
*Lynn Margaret Batten: ''Combinatorics of Finite Geometries''. Cambridge University Press 1986, ISBN 0-521-31857-2, p.&nbsp;1-22
 
==External links==
*[http://www.math.uni-kiel.de/geometrie/klein/math/geometry/partlin.html ''partial linear space''] at a website of the university of Kiel
*[http://planetmath.org/encyclopedia/PartialLinearSpace.html ''partial linear space''] at [[PlanetMath]]
 
[[Category:Geometry]]
 
 
{{geometry-stub}}

Latest revision as of 10:09, 9 January 2015

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