A Rank

1. A row of people or things organized in a grid pattern, often soldiers. Antonym: file
2. (chess) One of the eight horizontal lines of squares on a chessboard (i.e., those identified by a number). Antonym: file
3. (music) In a pipe organ, a set of pipes of a certain quality for which each pipe corresponds to one key or pedal.
4. One's position in a list sorted by a shared property such as physical location, population, or quality.
5. The level of one's position in a class-based society.
6. (typically in the plural) A category of people, such as those who share an occupation or belong to an organisation.
7. A hierarchical level in an organization such as the military.
8. (taxonomy) A level in a scientific taxonomy system.
9. (mathematics) The dimensionality of an array (computing) or tensor.
10. (linear algebra) The maximal number of linearly independent columns (or rows) of a matrix.
11. (algebra) The maximum quantity of D-linearly independent elements of a module (over an integral domain D).
12. (mathematics) The size of any basis of a given matroid.