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:
“There is special providence in the fall of a sparrow. If it be now, ‘tis not to come; if it be not to come, it will be
now; if it be not now, yet it will come—the readiness is
all.”
—William Shakespeare (1564–1616)
“There is nothing in the world that I loathe more than group activity, that communal bath where the hairy and slippery mix in a multiplication of mediocrity.”
—Vladimir Nabokov (1899–1977)