noun

• (cycling) A line of riders seeking maximum drafting in a crosswind, resulting in a diagonal line across the road.
  "In an echelon, in which several cyclists are sitting in on one another, each rider takes his turn of about 200 meters at the front before dropping to the rear."
• (military) A formation of troops, ships, aircraft, etc., in diagonal parallel rows.
  "The troops selected by his Royal Highness for this daring exploit, consisted of the war battalions of the 3d, 6th, and 7th regiments of the Royal Guard, forming the first echelon, […]"

verb

• (transitive, military) To form troops into an echelon.
  "July 1, Montcalm made a movement in advance, echeloning his troops from Fort Carillon to the foot of Lake George, to curb the enemy, and obstruct their landing."

adj

• (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.
  "An echelon matrix is a matrix, not necessarily square, with the following two properties: (i) There is at least one non-zero entry; rows consisting entirely of zeros, if any, lie below rows with at least one non-zero entry. (ii) In each non-zero row after the first, the left-most non-zero entry lies to the right of the left-most non-zero entry in the preceding row. […] In each of the non-zero rows of an echelon matrix, the left-most non-zero entry is called the pivot, […]"