# 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

## rank

a position in a SOCIAL STATUS hierarchy The familiar military usage reflects the wider use, which predates the language of social class.

## 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.
References in periodicals archive ?
But when Coral broke ranks just before Christmas last year, when new chief executive Nick Rust took over, and signed up to TurfTV, Hills and Ladbrokes followed within weeks, said Roth.
In the Senate, "Phil Gramm [of Texas] had actually succeeded in getting the votes necessary to nix new bailout money for the IMF, and it was [Nebraska Republican] Chuck Hagel who broke ranks and squirreled the deal," former Wall Street Journal Moscow correspondent Anne Williamson recalled to THE NEW AMERICAN.
On the day supporters nationwide paid their respects to Best by observing a minute's silence impeccably, Leeds fans who'd travelled to Millwall for a Championship clash broke ranks.
You chose to commend and display photos of the two Republican senators who broke ranks with their party to vote for the amendment.
A Chirac follower since his entry in politics at the tender age of fifteen, he broke ranks to support Balladur in the 1995 presidential election.
But one governor, prominent Christian Angela Sarkis, vice-president of the African Caribbean Evangelical Alliance, broke ranks and said she "profoundly disagreed" with the decision.
But one who broke ranks, Senator Michael Williams, said, "I expect him to be what he has always been--fair.
Labour MP Diane Abbott broke ranks and predicted that the Home Secretary would be leaving his post within weeks.
Twenty-seven Republicans broke ranks to oppose the measure, while 36 Democrats supported it.
Only the Northern League party broke ranks from the ruling centre-right coalition government to voice any opposition to the loan, but the move was supported by the opposition centre-left coalition.
Usdaw general secretary John Hannett said although few big stores opened on Christmas Day he feared in such a competitive industry if one company broke ranks others would follow.
During the war with Iraq, Spanish Prime Minister Jose Maria Anzar broke ranks with most of Europe by siding with the United States, which led to widespread public protest.

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