multiplication by a scalar
noun phraseUK /ˌmʌltɪplɪˈkeɪʃən baɪ ə ˈskeɪlə/
US /ˌmʌltəpləˈkeɪʃən baɪ ə ˈskeɪlər/
Multiplying by a scalar means making a vector or number bigger or smaller by timesing it by a single number.
Multiplying the vector (2, 3) by the scalar 4 gives (8, 12).
OTHER MEANINGS
2. In matrix algebra, multiplying every entry of a matrix by one number.
Multiplying the matrix by the scalar 3 triples each of its entries.
3. In physics, changing the size of a quantity such as force or velocity while keeping its direction.
Multiplying the velocity vector by the scalar 2 doubles its speed but keeps its direction.
4. A basic arithmetic idea where a single number is used to scale another value up or down.
In everyday math, multiplying a price by a scalar like 0.5 gives half the cost.