Matrices and the ability to work with them were introduced to handle problems involving larger amounts of data.

When a complex system contains, for example, nine parameters that can take different values (so-called “unknowns” or “variables”) and you know eight relationships between them (so-called “equations”), only a good, solid matrix — plus a few very simple operations — can save you.

That’s the thing about matrices: they are a very simple topic that can easily turn into a very difficult one. Simple, because they rely almost entirely on basic arithmetic you already know from school — addition, multiplication, and so on. Difficult, because the number of calculations can be large, and mistakes are easy to make.

There are quite a lot of operations you can perform with matrices, and it’s easy to get lost. There is no such thing as “computing a matrix” (it makes about as much sense as saying “computing a number”). You will add, subtract and multiply matrices, multiply them by numbers and by each other, transpose them, compute determinants, inverse matrices and ranks, and use them to solve systems of equations.

I hope that my lectures on this blog will help you get a good grasp of all of this.