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What is a matrix?

A matrix is simply a grid of numbers. That's all. If you've ever used a spreadsheet program, you've already met matrices in one form (matrices is just the plural of matrix).

For example, here's a 3×3 matrix consisting of a few random numbers that I just made up on the spot:

The above is an example of a square matrix, that is, a matrix containing the same number of rows as columns. But this doesn't have to be the case. For example, a 1×3 matrix (that's 1 row, 3 columns) looks like the following:

(12, 64.1, 64)

Have you read the section on vectors yet? If so, you might have noticed that the above, single row matrix, looks just like a typical 3-dimensional vector. Guess what? It is a vector. Vectors are just single row matrices! (The above vector is written horizontally - that's generally how vectors are written. But you can also write vectors vertically, as single column matrices, in which case they're called column vectors. The vector above is a row vector.)

What about a 1×1 matrix?

(6)

In this case, the brackets are unnecessary (the whole point of having the brackets there is to group multiple numbers together - there's no risk of a single number falling apart) and you can just write this as 6. Readers over the age of 2 months old will note that this looks just like an ordinary number (a scalar, if you've read the fundamentals section). That's because it is!

So, you see, matrices are just a logical extension of the ordinary scalar numbers you met when you first learned to count. Just as a vector is a scalar extended into multiple dimensions, a matrix is a scalar extended into multiple dimensions of multiple dimensions!

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