# Rank

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## rank

1
1. any of the eight horizontal rows of squares on a chessboard
2. Music a set of organ pipes controlled by the same stop
3. Maths (of a matrix) the largest number of linearly independent rows or columns; the number of rows (or columns) of the nonzero determinant of greatest order that can be extracted from the matrix

## rank

2
Botany showing vigorous and profuse growth

## Rank

1. J(oseph) Arthur, 1st Baron. 1888--1972, British industrialist and film executive, whose companies dominated the British film industry in the 1940s and 1950s
2. Otto . 1884--1939, Austrian psychoanalyst, noted for his theory that the trauma of birth may be reflected in certain forms of mental illness
Collins Discovery Encyclopedia, 1st edition © HarperCollins Publishers 2005

## rank

a position in a SOCIAL STATUS hierarchy The familiar military usage reflects the wider use, which predates the language of social class.
Collins Dictionary of Sociology, 3rd ed. © HarperCollins Publishers 2000
The following article is from The Great Soviet Encyclopedia (1979). It might be outdated or ideologically biased.

## Rank

in mathematics. The rank of a matrix is the order of a nonsingular minor of maximum order. It is also equal to the largest number of linearly independent rows or columns of the matrix. The rank remains unchanged under elementary transformations of the matrix—that is, when rows or columns are interchanged, when a row or column is multiplied by a nonzero number, and when rows or columns are added. A system of linear equations has a solution if and only if the rank of the matrix formed from the coefficients of the unknowns is equal to the rank of the augmented matrix, that is, the matrix formed by the addition of a column containing the constant terms to the coefficient matrix. This solution is unique if the rank is equal to the number of unknowns.

## Rank

(Russian, chin), the service position held by military personnel and civil servants, to which apply specified official rights and obligations. In prerevolutionary Russia, ranks were conferred according to the Table of Ranks, established by Peter I the Great. The concession of estate rights and privileges was connected with the attainment of a specific rank.

All civil and military ranks were abolished by the decrees of Soviet power of Nov. 10 (23) and Dec. 16 (29), 1917. Class ranks (chiny klassnye) have been established in the USSR for workers in the Procurator’s Office.

## Rank

a military formation in which servicemen are ranged side by side in a line. In a two-rank formation, the servicemen of one rank take a position one step behind the men of another rank; the front rank is called the first rank and the rear rank, the second. Both formations may be either close or open. In close formation the intervals between the men within a rank are equal to the width of a hand; in open formation the interval is one step or a distance ordered by the commander.

## rank

[raŋk]
(geology)
A coal classification based on degree of metamorphism.
(mathematics)
The rank of a matrix is its maximum number of linearly independent rows.
The rank of a system of homogeneous linear equations equals the rank of the matrix of its coefficients.
A tensor in an n-dimensional space is of rank r if it has n r components.
The rank of a group G is the number of elements in the basis of the quotient group of G over the subgroup consisting of all elements of G having finite period.
The rank of a place or valuation is equal to the number of proper prime ideals in its valuation ring.
The rank of a prime ideal P is the largest number n for which there exists a sequence P0= P, P1, P2, … , Pn of prime ideals such that Pi is a subset of Pi-1.
(mechanical engineering)
The number of rotational joints belonging to a robot.
(statistics)
The number assigned to an observation if a collection of observations is ordered from smallest to largest and each observation is given the number corresponding to its place in the order.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.
References in periodicals archive ?
We might say that the whole ear of late twentieth century society has been rankly abused by a forgery of the visual media.
Today Secret Service men, United States District Attorneys, United States Marshals, United States Court Commissioners, and other federal officials are rankly abusing their authority on every hand.
We want to feel our community as a fixed, continuous entity...as being anchored into the rock of permanence; but we know it's not, that in fact beneath the surface (or rankly all over the surface) it's anything but.
In such a climate of opinion, the gloomier sort of historicism flourishes as rankly as ragwort in an EC set-aside field, and right-wingers and leftists equally see Britain as effectively foredoomed to economic, social and political decline.
You see a multitude of hotels and taverns and stores, glaring with white paint, bedizened with placards and advertisements, and decorated by groups of those gentlemen who flourish most rankly on the soil of New York and in the vicinage of hotels; who carry their hands in their pockets, wear their hats always and every way, and, although of a stationary habit, yet spurn the earth with their heels.
I would fain be assured that I am growing apace and rankly, though my very growth disturb this dull equanimity,--though it be with struggle through long, dark, muggy nights or seasons of gloom.
Up on the slopes, the situation rankly doesn't took quite as bad as the environmentalists see it.
We think so; if your touch is a bit slapdash or even rankly amateur, it merely adds to a cobbler's homey, old-fashioned appeal.

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