Rank

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Related to ranks: Military ranks

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 classic literature ?
A truant provincial was paying the forfeit of his disobedience, by being plundered of those very effects which had caused him to desert his place in the ranks.
In that old day the English settler on these rude shores -- having left king, nobles, and all degrees of awful rank behind, while still the faculty and necessity of reverence was strong in him -- bestowed it on the white hair and venerable brow of age -- on long-tried integrity -- on solid wisdom and sad-coloured experience -- on endowments of that grave and weighty order which gave the idea of permanence, and comes under the general definition of respectability.
I wanted to keep my place by his side and not leave him under that rush of horses' feet, but it was in vain; and now without a master or a friend I was alone on that great slaughter ground; then fear took hold on me, and I trembled as I had never trembled before; and I too, as I had seen other horses do, tried to join in the ranks and gallop with them; but I was beaten off by the swords of the soldiers.
was the word that rang out, all down the long rank of the caravan.
I remember that, in 1838, many were waiting for the results of the West India experiment, before they could come into our ranks.
Delightful, charming, superior, first circles, spheres, lines, ranks, every thingand Mrs.
The teachers then shook hands with me and kissed me, and a murmur of pleasure ran through the ranks of my companions.
One end, indeed, reflected splendidly both light and heat from ranks of immense pewter dishes, interspersed with silver jugs and tankards, towering row after row, on a vast oak dresser, to the very roof.
Running in among them to swell the ranks, I was very near the chaise when it rolled away; and I had a lively impression made upon me, in the midst of the noise and dust, of having seen Mr.
I felt you start; you start as the regiment of the Bees started when Mopo walked before their ranks, and from the assegai in his hand the blood of Chaka[1] dropped slowly to the earth.
There was no want of distinguished and noble candidates to fill up the ranks on either side.
A subdued murmur of assent ran through the ranks of the Artisans, and Chromatistes, in alarm, attempted to step forward and address them.