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Operations on Vectors: Vector Addition

Vector addition superimposes vectors of the same dimension. It is calculated by adding together the elements in a particular position in each vector (see Figure 7a). In this way, multiple memories can be stored within the same vector.

Figure 7: (a) Vector Addition, (b) Matrix Addition.

Again vector addition can be extended to tensors of arbitrary rank (see figure 7b). Vector addition is expressed algebraically as a plus sign (+). So if we wanted to talk about the dot product of v with the addition of w and x we would write v.(w + x).

Another useful property to keep in mind is that the dot product distributes over addition. That is:

v.(w + x) = v.w + v.x