I read about it and did some googling, but didn’t really understand it. I was hoping someone here could break it down for me. I’d appreciate both examples and definitions on the terms, as well as of course, an explanation.
In: Mathematics
There are a lot of good explanations here on the difference in physical terms so I’ll add the mathematical part too.
A scalar is a single number. You see these all the time so you probably don’t need an example.
A vector is a set of numbers. They are usually written down as an array. For example:
[3,5,7]
or
[3,
5,
7]
the brackets in the second one usually go all the way from top to bottom but I don’t know how to do that in reddit. Those would be called 3×1 or 1×3 vectors, respectively.
Either a scalar or a vector can express many different things. When we’re working with physical objects we’re generally limited to 1×3 (3×1) or 1×4 (4×1) vectors. Each position would correspond to x,y,z and possibly time.
But we can also use vectors to represent other things. For example, if there are a bunch of candidates, a vector could be how many votes each candidate got in a particular state.
You can take the concept a step further and have a whole matrix. For example:
[3,5,7
6,4,2
3.5, 600,-676]
Those numbers can also correspond to all kinds of things. For example each row and column might represent a person in a class and each number might represent how much that person likes the other person (the diagonal row would probably be something like all 1 or all 0 in this case).
There are also a bunch of rules on how you can do math with scalars, vectors and matrices. That’s well outside the scope of an ELI5 though.
Latest Answers