rank

rank¹

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

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rank²

Botany showing vigorous and profuse growth

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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

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rank [raŋk]

(geology)

A coal classification based on degree of metamorphism.

stack

(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 ann-dimensional space is of rankrif it hasn^rcomponents.

The rank of a groupGis the number of elements in the basis of the quotient group ofGover the subgroup consisting of all elements ofGhaving 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 idealPis the largest numbernfor which there exists a sequenceP₀=P,P₁,P₂, … ,P_nof prime ideals such thatP_iis a subset ofP_i-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.