Who decided to multiply matrix in such a weird way and for which reason ?
In: Mathematics
A matrix is one possible way to represent a system of linear equations. So if you have a vector of numbers v and a system of linear equations represented by A, then applying that system of linear equations to the vector results in the vector Av.
But what if you have two systems of linear equations and want to apply one after the other? This can actually be done with a single system of linear equations. Matrix multiplication is defined such that it performs this combination. So if your systems of linear equations are represented by matrices A and B and you want to apply first B and then A to a vector v, then matrix multiplication is defined such that A(Bv)=(AB)v.
So essentially, matrix multiplication as defined as it is allows you to combine multiple sequential systems of linear equations into a single system of linear equations.
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