In mathematics, the meaning of scalar depends on the context; it can refer to real numbers or complex numbers or rational numbers, or to members of some other specified field. Generally, when a vector space over the field F is studied, then F is called the field of scalars. A scalar is formally a tensor of rank zero.
In physics a scalar is a quantity that can be described by a single number (either dimensionless, or in terms of some physical quantity). Scalar quantities have magnitude, but not a direction and should thus be distinguished from vectorss. More formally, a scalar is a quantity that is invariant under coordinate rotations (or Lorentz transformations, for relativity).
Examples of (non-relativistic) scalar quantities include:Latin for "ladder" and means "resembling a ladder". According to a citation in the Oxford English Dictionary the first usage of the term (by W. R. Hamilton in 1846) described it as:
- "The algebraically real part may receive, according to the question in which it occurs, all values contained on the one scale of progression of numbers from negative to positive infinity; we shall call it therefore the scalar part."