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In mathematics, particularly in semigroup theory, a transformation is any function ''f'' mapping a set ''X'' to itself, i.e. ''f'':''X''→''X''. In other areas of mathematics, a transformation may simply be any function, regardless of domain and codomain. This wider sense shall not be considered in this article; refer instead to the article on function for that sense. Examples include linear transformations and affine transformations, rotations, reflections and translations. These can be carried out in Euclidean space, particularly in dimensions 2 and 3. They are also operations that can be performed using linear algebra, and described explicitly using matrices. ==Translation== (詳細はaffine transformation of Euclidean space which moves every point by a fixed distance in the same direction. It can also be interpreted as the addition of a constant vector to every point, or as shifting the origin of the coordinate system. In other words, if v is a fixed vector, then the translation ''T''v will work as ''T''v(p) = p + v. For the purpose of visualization, consider a browser window. This window, if maximized to full dimensions of the screen, is the reference plane. Imagine one of the corners as the reference point or origin (0, 0). Consider a point ''P''(''x'', ''y'') in the corresponding plane. Now the axes are shifted from the original axes to a distance (''h'', ''k'') and this is the corresponding reference axes. Now the origin (previous axes) is (''x'', ''y'') and the point P is (''X'', ''Y'') and therefore the equations are: ''X'' = ''x'' − ''h'' or ''x'' = ''X'' + ''h'' or ''h'' = ''x'' − ''X'' and ''Y'' = ''y'' − ''k'' or ''y'' = ''Y'' + ''k'' or ''k'' = ''y'' − ''Y''. Replacing these values or using these equations in the respective equation we obtain the transformed equation or new reference axes, old reference axes, point lying on the plane. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Transformation (function)」の詳細全文を読む スポンサード リンク
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