## Linear Combination of Vectors

A linear combination of vectors is a sum of scalar multiples of those vectors. That is, given a set of vectors of the same type,5.4 such as (they must have the same number of elements so they can be added), a linear combination is formed by multiplying each vector by a scalar and summing to produce a new vector of the same type:

For example, let , , , and . Then the linear combination of and is given by

In signal processing, we think of a linear combination as a signal mix. Thus, the output of a mixing console may be regarded as a linear combination of the input signal tracks.

Next Section:
Linear Vector Space
Previous Section:
Scalar Multiplication