In mathematics, the special linear group of degree n over a field F is the set of n × n 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, 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).
Read more about Special Linear Group: Geometric Interpretation, Lie Subgroup, Topology, Relations To Other Subgroups of GL(n,A), Generators and Relations, Structure of GL(n,F)
Famous quotes containing the words special and/or group:
“Fashions change, and with the new psychoanalytical perspective of the postwar period [WWII], child rearing became enshrined as the special responsibility of mothers ... any shortcoming in adult life was now seen as rooted in the failure of mothering during childhood.”
—Sylvia Ann Hewitt (20th century)
“The trouble with tea is that originally it was quite a good drink. So a group of the most eminent British scientists put their heads together, and made complicated biological experiments to find a way of spoiling it. To the eternal glory of British science their labour bore fruit.”
—George Mikes (b. 1912)