Jordan decomposition in an affine algebraic group
= Jordan decomposition in an affine algebraic group
{c}
{wiki=Jordan–Chevalley_decomposition}
Every element $g$ of an affine algebraic group has unique commuting semisimple and unipotent parts $g_s,g_u$ such that $g=g_sg_u$. The construction agrees with the multiplicative <Jordan normal form>[Jordan decomposition] in every rational representation.