echelon

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

Other important functions performed by the GP [general practitioner] are those of referring patients to other (health) care facilities and acting as contact person for other providers of aid, both for other facilities in first echelon care and with respect to second echelon care (outpatient care and treatment in hospital).

Officials in China are divided into three echelons, or generations. The first echelon joined the Communist Party in the 1920s, soon after the party was founded. […] The second echelon joined the Communist Party before the founding of the People's Republic of China in 1949. The party was then still struggling, and many of the second echelon died during the wars. They were again true patriots. The third echelon joined the Communist Party after the founding of the People's Republic.

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.

Cyclists in an echelon take up more room in the traffic lane than they do when riding single or double file.

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, […]

The order in echelons is favorable for attack, because it readily conforms to the nature of the ground, and does not necessitate engaging more than a part of the forces; it is adopted for the purpose of attacking a particular point of the enemy's line.

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.

Behind the 17th Panzer Division the corps echeloned the main force of its other division, the 16th Panzer Division.

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 s

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, […]