A scalar is any constant value used as a scale factor applied to a vector. Mathematically, all of our scalars will be either real or complex numbers.5.3 For example, if denotes a vector of complex elements, and denotes a complex scalar, then
In signal processing, we think of scalar multiplication as applying some constant scale factor to a signal, i.e., multiplying each sample of the signal by the same constant number. For example, a 6 dB boost can be carried out by multiplying each sample of a signal by 2, in which case 2 is the scalar. When the scalar magnitude is greater than one, it is often called a gain factor, and when it is less than one, an attenuation.
Linear Combination of Vectors