Abstract
One of the most beautiful results in early linear algebra is that every matrix over an algebraically closed field is similar to a Jordan matrix. This, of course, immediately proves that the Borel subgroup (the subgroup consisting of invertible n × n upper triangular matrices) is conjugate dense in GLn(ℂ). However, other matrices are also conjugate dense in GLn(ℂ). In this article, we show that a variation of Pascal matrices are one such class of conjugate dense matrices. We then use this fact to reduce finding matrix powers, roots, and inverses down to the corresponding problem for an appropriately chosen diagonal matrix. Having done this, we explore how one might create a wide array of other conjugate dense subgroups of GLn(ℂ).