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 ?
property based on the rankest of hearsay and the flimsiest of
After all, determining what is true and false in political campaigns can be notoriously difficult (64) given that in politics, in the Court's own words, "the tenets of one man may seem the rankest error to his neighbor.
Indeed the first over, bowled by Andrew Davies, was a maiden and when Wagh pulled the rankest of long-hops straight to the only man on the leg-side boundary and Ian Bell gloved a pull, it looked as if the visitors would struggle to set a testing target.
As a young man he had been "steeped in the rankest romantic literature of Germany," as he recalled later in life--but he was wise enough soon to be "acutely aware of the mischief done me.
This amounts to the rankest form of racial profiling," said Adam Schwartz, a staff attorney for the American Civil Liberties Union of Illinois.
53) Such logic can cast as "the rankest essentialism" (54) any claim whatsoever that race exists.
Writing exclusively for the Daily Post, Jonathan Margolis describes an article he wrote on the eve of James Bulger's funeral in 1993, as ``one of the rankest anti-Liverpool articles ever to emerge from Fleet Street''.
He insists that tax breaks can go to religious schools that engage in the rankest forms of racial discrimination.
The Court stressed that the only legislative history that counted for Section 5 purposes was that found in the record of congressional action that documented actual constitutional violations by states against disabled employees--evidence from the private sector or even from local governments (which are not protected by Eleventh Amendment immunity), even if it revealed the rankest discrimination against disabled workers, was declared irrelevant.
Even the rankest amateur hunter can get lucky and shoot a world record animal.
dissenting) ("There is no showing, but only the rankest of speculation, that a reduction or even complete destruction of the viability of the Delhi Sands Flower.
This is post hoc propter hoc reasoning at its rankest, and is contrary to the "hard look" encouraged and even required by our case law.

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