When do you decide to represent something as a vector?

Question

In information retrieval, the words in the documents were represented as a "Term Vector", they did it primarily to check the angle between two vectors. When have you represented something as a vector in your work and what is the common heuristic that you use to represent an entity as a vector?

Answer 1

In programming Vector usually refers to graphic related issues. In Mathematics a vector is a member of a set that has some special structure attached to it. This set is called a Vector Space.

Linear algebra is the Algebra that deals with vector spaces and it provides many useful results that can benefit programming a lot.

If you are interested you should read on Linear Algebra on line. Any search will give you sufficient results. Also i think MIT offers some of its classes as free downloads, I'm sure you can find something with quality there.

Answer 2

It all depends, really; in fact, in some languages, there are objects called "vectors" that aren't actually vectors in the mathematical sense (example: Java), and the term "vector" is also used for lots of unrelated stuff. See here: http://en.wikipedia.org/wiki/Vector#In_computer_science.

And then there are all the ways vectors are used in math and physics: http://en.wikipedia.org/wiki/Vector_(mathematics_and_physics).

Personally, I would use a vector (as in, the sort with both direction and magnitude) when working with things that require both a direction and a magnitude, such as force, velocity, acceleration, and the like, as well as other situations when the ability to perform dot products and cross products is useful. Otherwise, you're basically just using a set of values grouped together, such as coordinates for a point in space; in a sense, a specific sort of array.

Of course, this isn't even considering such things as tensors and other related concepts, which are on another level entirely.