THE LIE GROUP OF UMBRELLA MATRICES AND PAIRWISE COMPARISONS MATRICES.

In this paper, we work with the umbrella matrix Lie group and its Lie algebra. We show that the Lie subalgebra of the PC matrix is the Lie algebra of the umbrella matrix. Furthermore, we obtain an isomorphism between the Lie subgroup of PC matrices and the umbrella matrix Lie group. [ABSTRACT FROM AUTHOR]