Definition of "echelon" in English

noun

1. A level or rank in an organization, profession, or society.

2. (cycling) A line of riders seeking maximum drafting in a crosswind, resulting in a diagonal line across the road.

3. (military) A formation of troops, ships, aircraft, etc., in diagonal parallel rows.

verb

1. (transitive, military) To form troops into an echelon.

adjective

1. (linear algebra) 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.