An orthogonal basis for computing a consistent approximation to a pairwise comparisons matrix

The algorithm for finding a consistent approximation to an inconsistent pairwise comparisons matrix is based on a logarithmic transformation of a pairwise comparisons matrix into a vector space with the Euclidean metric. An orthogonal basis is introduced in the vector space formed by the images of consistent matrices. The required consistent approximation is the orthogonal projection of the transformed matrix onto this space.