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When you multiply two matrices together I have been told you get something similar. I hear that this is because a matrix can be treated as a vector.

So if we are talking about measurable things, in the real world does matrix multiplication have any relevance ?

I might be off the mark but what if we were to build a model, based on height weight and income would that be definable in 3 dimensions and therefore if you had two sets of observation and you multiplied them the answer would be nonsense but somehow it has a definition in 3 dimensions as a new matrix ?

if for example, i had a range of multiplies I wanted to apply to each observation or set of observations, stored in a matrix then this would be a scalar multiplication of a matrix onto another matrix ? Does such a thing exist.

Apologies I am not a mathematician so my terminology is buggered but I'm still curious.

Thanks,