Echelon meaning : A level or rank in an organization, profession, or society. A line of riders seeking maximum drafting in a crosswind, resulting in a diagonal line across the road. A formation of troops, ships, etc., in diagonal parallel rows. To form troops into an echelon. Of a matrix: having undergone Gaussian elimination with the result that the leading coefficient or pivot (that is, the first nonzero number from the left) of a nonzero row is to the right of the pivot of the row above it, giving rise to a stepped appearance in the matrix.