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Scalar multiplication
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).
==Definition==
In general, if ''K'' is a field and ''V'' is a vector space over ''K'', then scalar multiplication is a function from ''K'' × ''V'' to ''V''.
The result of applying this function to ''c'' in ''K'' and ''v'' in ''V'' is denoted ''cv''.
抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』
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