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:
“Myths, as compared with folk tales, are usually in a special category of seriousness: they are believed to have “really happened,” or to have some exceptional significance in explaining certain features of life, such as ritual. Again, whereas folk tales simply interchange motifs and develop variants, myths show an odd tendency to stick together and build up bigger structures. We have creation myths, fall and flood myths, metamorphose and dying-god myths.”
—Northrop Frye (1912–1991)
“I can’t think of a single supposedly Black issue that hasn’t wasted the original Black target group and then spread like the measles to outlying white experience.”
—June Jordan (b. 1936)