純粋・応用数学（含むガロア理論）3

純粋・応用数学（含むガロア理論）3at MATH

純粋・応用数学（含むガロア理論）3 - 暇つぶし2ch606:l_linear_group General linear group (抜粋) In mathematics, the general linear group of degree n is the set of n×n invertible matrices, together with the operation of ordinary matrix multiplication. This forms a group, because the product of two invertible matrices is again invertible, and the inverse of an invertible matrix is invertible, with identity matrix as the identity element of the group. The group is so named because the columns of an invertible matrix are linearly independent, hence the vectors/points they define are in general linear position, and matrices in the general linear group take points in general linear position to points in general linear position. To be more precise, it is necessary to specify what kind of objects may appear in the entries of the matrix. For example, the general linear group over R (the set of real numbers) is the group of n×n invertible matrices of real numbers, and is denoted by GLn(R) or GL(n, R). つづく

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