a body of troops arranged in a line
"The general ordered his soldiers to form an echelon along the ridge before advancing toward the enemy."
a diffraction grating consisting of a pile of plates of equal thickness arranged stepwise with a constant offset
"The physicist adjusted the echelon by sliding the stack of glass plates to create the precise interference pattern needed for the experiment."
A level or rank in an organization, profession, or society.
"She quickly rose through the corporate echelons to become the company's youngest CEO."
To form troops into an echelon.
"The general ordered his cavalry to move into a diagonal line, forming them into an echelon before advancing on the enemy."
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.
"The professor explained that after applying Gaussian elimination, the resulting echelon form revealed a clear staircase pattern where each leading coefficient sat strictly to the right of the one above it."
An international SIGINT network to monitor and gather intelligence from satellite trunk communications.
"Intelligence analysts rely on Echelon to intercept classified data flowing through global satellite networks."