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:
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—National Woman’s Party, quoted in Everyone Was Brave. As, ch. 8, by William L. O’Neill (1969)
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—Anna Quindlen (b. 1953)