Ranks meaning : 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"]. 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 The level of one's position in a class-based society A hierarchical level in an organization such as the military A level in a scientific taxonomy system 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. To assign a suitable place in a class or order; to classify. To take rank of; to outrank.