ranks

A row of people or things organized in a grid pattern, often soldiers [the corresponding term for the perpendicular columns in such a pattern is "file"].

“The front rank kneeled to reload while the second rank fired over their heads.”

In a pipe organ, a set of pipes of a certain quality for which each pipe corresponds to one key or pedal.

One's position in a list sorted by a shared property such as physical location, population, or quality

“Based on your test scores, you have a rank of 23.”

The level of one's position in a class-based society

A hierarchical level in an organization such as the military

“He rose up through the ranks of the company, from mailroom clerk to CEO.”

A level in a scientific taxonomy system

“Phylum is the taxonomic rank below kingdom and above class.”

Maximal number of linearly independent columns (or rows) of a matrix.

The dimensionality of an array or tensor.

The maximum quantity of D-linearly independent elements of a module (over an integral domain D).

The size of any basis of a given matroid.

One of the eight horizontal lines of squares on a chessboard (i.e., those identified by a number). The analog vertical lines are the files.

(typically in the plural) A category of people, such as those who share an occupation.

To place abreast, or in a line.

To have a ranking.

“Their defense ranked third in the league.”

To assign a suitable place in a class or order; to classify.

To take rank of; to outrank.