echelons

Echelon is a term used to describe a level or rank in a hierarchical organization, or a layer arranged in a stepped formation. It can refer to a tier within a structure, from senior leadership to subordinate units, as well as to the steps or layers in processes and systems. The word derives from the French échelon, meaning a rung of a ladder, and entered English in the early modern period. It is commonly used in military, business, and government contexts to indicate relative position or arrangement along a chain of command or sequence of steps.

In military usage, an echelon describes a staggered formation in which units are offset along a line of march, such as echelon left or echelon right. Such formations can increase firepower, mutual support, or mobility, and are selected for tactical reasons including protection of the flank and distribution of risk. The term also extends to organizational structures, where echelons denote levels of command, responsibility, or decision-making, from top management to frontline staff. In this sense, the term emphasizes the hierarchical character of an institution or process.

In mathematics, echelon form refers to a standardized representation of a matrix. Row echelon form requires that all nonzero rows appear above any rows of zeros, and that the leading entry of each nonzero row is to the right of the leading entry of the row above it. Reduced row echelon form strengthens this by requiring that the leading entries be 1 and that all other entries in the pivot columns be zero.

Beyond these domains, echelons appear in discussions of organizational theory, project management, and logistics to describe strata of authority, responsibility, or sequential steps.