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Flat (geometry)
In geometry, a flat is a subset of that is congruent to a Euclidean space of lower dimension. The flats in two-dimensional space are points and lines, and the flats in three-dimensional space are points, lines, and planes.
In -dimensional space, there are flats of every dimension from 0 to .〔In addition, all of -dimensional space is sometimes considered an -dimensional flat as a subset of itself.〕 Flats of dimension are called hyperplanes.
Flats are similar to linear subspaces, except that they need not pass through the origin. If Euclidean space is considered as an affine space, the flats are precisely the affine subspaces. Flats are important in linear algebra, where they provide a geometric realization of the solution set for a system of linear equations.
A flat is also called a ''linear manifold'' or ''linear variety''.
==Descriptions==
抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』
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