Evolutionary processes such as migration, genetic drift, and natural selection are thought to play a prominent role in species invasions into novel environments. However, few empirical studies have explored the mechanistic basis of invasion in an evolutionary framework. One promising tool for inferring evolutionarily important changes in introduced populations is the genetic variance-covariance matrix (G matrix). G matrix comparisons allow for the inference of changes in the genetic architecture of introduced populations relative to their native counterparts that may facilitate invasion. Here, we compare the G matrices of reed canarygrass (Phalaris arundinacea L.) populations across native and invasive ranges, and between populations along a latitudinal gradient within each range. We find that the major differences in genetic architecture occur between populations at the Northern and Southern margins within each range, not between native and invasive populations. Previous studies have found that multiple introductions in introduced populations caused an increase in genetic variance on which selection could act. In addition, we find that differences in the evolutionary potential of Phalaris populations are driven by differences in latitude, suggesting that selection also shapes the evolutionary trajectory of invasive populations.