Statistics Dictionary

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Linear Combination of Vectors

If one vector is equal to the sum of scalar multiples of other vectors, it is said to be a linear combination of the other vectors.

For example, suppose a = 2b + 3c, as shown below.

11
16
   =   
1
2
   +   
3
4
   =   
2*1 + 3*3
2*2 + 3*4
a b c

Note that 2b is a scalar multiple and 3c is a scalar multiple. Thus, a is a linear combination of b and c.

See also:  Vector Dependence | Matrix Rank