Phylogeny is an important field to understand evolution and the organization of life. However, most methods depend highly on manual study and analysis, making the construction of phylogeny error prone. Linear Algebra methods are known to be efficient to deal with the semantic relationships between a large number of elements in spaces of high dimensionality. Therefore, they can be useful to help the construction of phylogenetic trees. The ability to visualize the relationships between genomes is crucial in this process. In this paper, a linear algebra method, followed by optimization, is used to generate a visualization of a set of complete genomes. Using the proposed method we were able to visualize the relationships of 64 complete mitochondrial genomes, organized as six different groups, and of 31 complete mitochondrial genomes of mammals, organized as nine different groups. The prespecified groups could be seen clustered together in the visualization, and similar species were represented close together. Besides, there seems to be an evolutionary influence in the organization of the graph.