Sum of the products of the elements in a set V of mathematical objects by the elements in a set S of
scalars.
Example
If the variables
x and
y belong to a set of
real numbers and
a and
b are integers, then the expression
[latex]z = ax + by[/latex]
represents the real number
z in the form of
a linear combination of the integers
a and
b.
Educational Note
The concept of a linear combination refers to two sets V and S of mathematical objects, which are
vectors in a
vector space and numbers or scalars in a numerical space, such as the set of real numbers. We define an external operation so that every element of V can be expressed as a sum of the products of a
scalar of S and a vector of V. The number of terms in this product depends on the dimension of the chosen vector space. If the vector space is 2-dimensional, then each linear combination will include 2 terms; if the vector space is 3-dimensional, then each linear combination will include 3 terms; and so on.
