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A scalar is any real number, or any quantity that can be measured using a single real number.
Contents
Examples
Temperature, length, and mass are all scalars.
Description
A scalar is said to have magnitude but no direction.
Vectors and vector spaces
A quantity with both direction and magnitude, such as force or velocity, is called a vector.
In linear algebra, real numbers are called scalars and relate to vectors in a vector space through the operation of scalar multiplication, in which a vector can be multiplied by a number to produce another vector.
More generally, a vector space may be defined by using any field instead of real numbers, such as complex numbers. Then the scalars of that vector space will be the elements of the associated field.
Scalar product operations
A scalar product operation – not to be confused with scalar multiplication – may be defined on a vector space, allowing two vectors to be multiplied to produce a scalar. A vector space equipped with a scalar product is called an inner product space.
Quaternions
The real component of a quaternion is also called its scalar part.
Informal use
The term is also sometimes used informally to mean a vector, matrix, tensor, or other usually "compound" value that is actually reduced to a single component. Thus, for example, the product of a 1×n matrix and an n×1 matrix, which is formally a 1×1 matrix, is often said to be a scalar.
Scalar matrix
The term scalar matrix is used to denote a matrix of the form kI where k is a scalar and I is the identity matrix.
See also
External links
- Scalar (mathematics) @ Wikipedia
