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On the application of matrices to the 'everyday life'

Email answer to a friend (studying management) who asked me recently, and then again yesterday, to teach her about matrices and how to apply them to every day life...

You asked me a question yesterday about matrices and I just want to make sure that the answer that I gave to you is clear. You asked me to teach you about matrices and explain to you how to apply them to "every day life".

In mathematics we have what we call "number systems", they are particular conventions allowing us to perform some computations using things that we call "numbers". For instance, the set of integers is a number system and allows you to perform computations on, say, marbles. If you have two marbles and then give three more to you, you have in mind the concept of the number "five", which allows you to keep track of how many marbles you then have. The set of real numbers (number with decimal digits) is another number system, which allows us to consider quantities that are not necessarily whole integers, such as tracking the air temperature for instance (that was really just an example). The collection of matrices is also a number system. I explained the rules of the algebraic manipulation of matrices, but there is nothing else I can really do. By the way. there are lots of other number systems that one can know about and which are studied in mathematics, the algebra of complex numbers is another one that is sometimes studied in high school. There are also numbers system related to the way us human count time (you use them everyday without really noticing).

Depending on the area that you work in, depending on the problems that you have to solve, you may decide that matrices are the best number system to perform your computations (of course this can be justified if your problem has an internal structure matching the internal algebraic rules of the algebra of matrices). If you study and work in areas (such as management) where none of the problems you will be considering needs to use matrices, then you will simply never use them during your entire life.

If you were a theoretical physicist, for instance, then you would be using them quite often. The behavior of many sub-atomic particles, for instance, can be modeled using matrices.