Decomposition of matrices into commutators of involutions
Let \(\text{SL}_nF\) be the special linear group over some field \(F\). An element \(T\) in \(\text{SL}_nF\) is called an involution if \(T^2=1\). A matrix \(A\) in \(\text{SL}_nF\) is called a commutator of involutions if there are two involutions \(S\) and \(T\) in \(\text{SL}_nF\) such that \(A=TST^{-1}S^{-1}\). The author shows: If \(F\) is the complex number field or the real number field, then every matrix \(A\) in \(\text{SL}_nF\) is either a commutator of involutions or it can be written as a product of two commutators of involutions. Not every element \(A\) is a commutator of involutions.
scientific article; zbMATH DE number 1790221