General linear group
... Over a field F, a matrix is invertible if and only if its determinant is nonzero. Therefore an alternative definition of GL(n, F) is as the group of matrices with nonzero determinant. Over a commutative ring R, one must be slightly more careful: a matrix over R is invertible if and only if its deter ...
... Over a field F, a matrix is invertible if and only if its determinant is nonzero. Therefore an alternative definition of GL(n, F) is as the group of matrices with nonzero determinant. Over a commutative ring R, one must be slightly more careful: a matrix over R is invertible if and only if its deter ...
