Support Vector Machines — Lecture series — Dot product

In the previous post, we spoke about the direction of a vector and how to ascertain the direction of a vector of given magnitude. In this post, we would be talking about the dot product of a vector.

Learning objective:

Understand the main idea behind what a dot product is.

Main question:

Consider the 2 vectors in Fig. 1 below:

Fig 1

How much are these 2 vectors pointing in the same direction?

Another way to interpret this question is, “how much does one vector overlap with the other vector”?

To answer this question, we would have to make the following observation:

The direction of the vector ‘a’ can be reached by going in the direction of the of the vector ‘b’ up to a certain point and subsequently moving in the perpendicular direction. This is demonstrated in Fig 2 below:

Fig. 2

Therefore vector ‘a’ and ‘b’ are moving in the same direction by the amount of direction that you had to move in the direction of vector ‘b’ before you branched out to move perpendicularly.

This is what the dot product of a vector is all about. It helps us to obtain an accurate measurement of how two vectors are moving in the same direction by telling us how much one vector moves in the direction of the other vector before branching out in a perpendicular direction towards that vector.

In the next post, we would look at how to actually calculate the dot product :)