Algebra plays a bigger role in computing than expected. A few beginner rogrammers may notice that variables can be manipulated similarly to variables in algebra. For instance, adding five to a number which is defined by a function. What I am focusing on is the idea of a matrix and how that can be used in programming.

In pure maths, a matrix is a collection of vectors. However it can be used in other ways. It may be used as a 'table' of values. Let's assume we want to represent profit per quarter over four years. We could let each row equal the quarter and column equal year so that we form a 4 by 4 square matrix. This is exactly the same as creating a multidimensional array. This can be proven by the fact that this sort of array can be represented geometrically in two dimensions. This is similar to a matrix.

But that is just one use. We could use it in encryption.

Suppose we want to encrypt the password "password" to be stored in a database.

If we allow each letter of the alphabet to be equal to a number corresponding to its position such that

a=1 b=2 c=3 ...

Then our password can be rewritten as

16 1 19 19 23 15 18 4

We can split this into three groups of three numbers each (if less than three number are in a group then the value of the missing number(s) is zero.) We should end up with nine numbers in three groups. By allowing the first number of each group to be in row one - ordered by group umber - and continuing in this fashion we get the matrix

16 19 18
1 23 4
19 15 0

The next step is to multiply by an encoding matrix. Because this has an infinite amount of values, it is hard to undo this encryption from a hacking perspective. We'll let this matrix equal

-3 -3 -4
0 1 1
-4 3 4

So that the product is

-120 25 27
-19 32 35
-57 -42 -61

If we reverse the process for converting the text into a matrix, our encrypted password is

-120 -19 -56 25 32 -42 27 35 -61

A hacker seeing this would have a hard time seeing what these numbers mean. Even if he realised it came from a matrix multiplication he'd have to work out the encoding matrix. Plus we could make a more sophisticated method for assigning numbers to letters making our encryption more dense. We could also make the encoding matrix dependant on what was inputted so it is harder to guess it.

The major advantage of this is that it's easy to decode with the inverse of the encoding matrix since this multiplied by the product to return to our original matrix.

I will post other uses of maths in future blogs butt for now, adios.