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In mathematics, the special linear group of degree ''n'' over a field ''F'' is the set of matrices with determinant 1, with the group operations of ordinary matrix multiplication and matrix inversion. This is the normal subgroup of the general linear group given by the kernel of the determinant : where we write ''F''× for the multiplicative group of ''F'' (that is, ''F'' excluding 0). These elements are "special" in that they fall on a subvariety of the general linear group – they satisfy a polynomial equation (since the determinant is polynomial in the entries). ==Geometric interpretation== The special linear group can be characterized as the group of ''volume and orientation preserving'' linear transformations of R''n''; this corresponds to the interpretation of the determinant as measuring change in volume and orientation. 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「special linear group」の詳細全文を読む スポンサード リンク
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