In
mathematics,
scalar multiplication is one of the basic operations defining a
vector space in
linear algebra (or more generally, a
module in
abstract algebra). In an intuitive geometrical context, scalar multiplication of a
real Euclidean vector by a positive real number multiplies the magnitude of the vector without changing its direction. The term
"scalar" itself derives from this usage: a scalar is that which
scales vectors. Scalar multiplication is the multiplication of a vector by a scalar (where the product is a vector), and must be distinguished from
inner product of two vectors (where the product is a scalar).