# What is an eigenvector?

During the ‘pair-wise’ voting process, individuals provide a vote/judgment on the degree of relative importance of each criterion against the others. The group average for each paired criteria comparison (i.e., each pair-wise vote) is found using the geometric mean.* Once the votes for each paired comparison is cast in the pair-wise process, the group averages are pulled into a single matrix. *A geometric mean is used because it captures the relative scoring relationships from the comparisons (a geometric mean is defined as the nth root of the product of n numbers) - The matrix is then raised to a power (multiplied against itself) to determine the ‘Eigenvector,’ or vector of priorities. As the matrix is multiplied against itself multiple times, the Eigenvector of each successive matrix changes less and less until it converges on one stable Eigenvector (Decision Lens multiplies the matrix against itself 32 times, or less if stability is achieved after fewer multiplications). These figures become the criteria weights that are displayed on the priority graph.