# scalar

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## scalar,

quantity or number possessing only sign and magnitude, e.g., the real numbers (see numbernumber,
entity describing the magnitude or position of a mathematical object or extensions of these concepts. The Natural Numbers

Cardinal numbers describe the size of a collection of objects; two such collections have the same (cardinal) number of objects if their
), in contrast to vectorsvector,
quantity having both magnitude and direction; it may be represented by a directed line segment. Many physical quantities are vectors, e.g., force, velocity, and momentum.
and tensorstensor,
in mathematics, quantity that depends linearly on several vector variables and that varies covariantly with respect to some variables and contravariantly with respect to others when the coordinate axes are rotated (see Cartesian coordinates).
; scalars obey the rules of elementary algebra. Many physical quantities have scalar values, e.g., length, area, mass, energy, and electric charge. Such quantities as velocity, force, momentum, and spin are vectors and follow different algebraic rules.
The following article is from The Great Soviet Encyclopedia (1979). It might be outdated or ideologically biased.

## Scalar

a quantity such that each of its values can be expressed by a single (real) number. Examples of scalars include length, area, time, mass, density, temperature, and work. The term “scalar” is used—sometimes simply as a synonym for “number”—in vector analysis, where a scalar is distinguished from a vector.

## scalar

[′skā·lər]
(computer science)
A single value or item.
(mathematics)
One of the algebraic quantities which form a field, usually the real or complex numbers, by which the vectors of a vector space are multiplied.
(physics)
A quantity which has magnitude only and no direction, in contrast to a vector.
A quantity which has magnitude only, and has the same value in every coordinate system. Also known as scalar invariant.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.

## scalar

1. a quantity, such as time or temperature, that has magnitude but not direction
2. Maths an element of a field associated with a vector space
3. having magnitude but not direction
Collins Discovery Encyclopedia, 1st edition © HarperCollins Publishers 2005

## scalar

(mathematics)
A single number, as opposed to a vector or matrix of numbers. Thus, for example, "scalar multiplication" refers to the operation of multiplying one number (one scalar) by another and is used to contrast this with "matrix multiplication" etc.

## scalar

(architecture)
In a parallel processor or vector processor, the "scalar processor" handles all the sequential operations - those which cannot be parallelised or vectorised.