The method described in this article is a modified QR factorization. The matrices being used represent proteins, which allow the authors of the article to examine “the phylogenetic tree topology of the homologous group.” In order to do this, the QR factorization we learned in class was first modified to work with multiple dimensions matrices. In making the QR factorization for each matrix, a basis set of protein structures was made, which spans the “evolutionary space.”

Having this basis set of protein structures allows for the information in things such as genome sequences to be much more easily analyzed. According to the article, there is widespread agreement that a basis set such as the one found with the QR factorization is needed. The article makes an argument that the QR factorization provides the best basis for the purposes of being able to analyze bioinformatics much more efficiently. The authors believe this to be true because the QR factorization stores the most linearly independent in the first columns of Q. While there is no specific way of determining linear independence of protein structures, having them sorted in this way allows for the information to be used much more easily. Essentially what happens is the most frequently used protein structures are stored in the lower numbered columns of the Q matrix, while the ones used rarely are in higher numbered columns.