Craig, Homer V. Department of Mathematics, University of Texas, Austin, Texas.
Last reviewed:August 2020
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A term synonymous in mathematics with “real” in real number or real function. The magnitude of a vector two units in length is the real number or scalar 2. The dot or scalar product of two vectors is the product of three real numbers associated with them (the magnitude of the first vector times the magnitude of the second, times the cosine of the angle between them) and is therefore a scalar. If in the functional relationships S = S(x, y, z), F = F(x, y, z), S is a real number and F is a vector, then S(x,y,z) is a scalar function but F(x, y, z) is a vector function. More generally, if V is a vector space over a field F, the elements of F are often referred to as scalars. See also: Calculus of vectors; Linear algebra
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