Transvections generate the special linear group
= Transvections generate the special linear group
Row additions reduce an invertible matrix to diagonal form without changing determinant. A determinant-one diagonal matrix is a product of diagonal two-coordinate blocks $\operatorname{diag}(a,a^{-1})$, each expressible as a product of six <elementary transvection matrices>. Therefore these matrices generate the <special linear group> over a field.
// Target: algebra.bigb