Matrix Multiplication in Real Life

Hello World,

Let me start this discussion with a basic question. What does simple multiplication means?

To me, it feel like this. Say your IQ is 120. You have a magic wand, you wave it and say “Let my IQ go twice”. With multiplication, you can grow or shrink some quantity as you wish.

Suppose I am having a Rs. 1000/- note in my purse and if  I wish that “Let my amount in purse go 1.5 x” will turn the Rs. 1000/- to Rs. 1500/- ))

We can’t multiply things that don’t exist. I don’t have a private Jet Air plane so does I can’t multiply it.

This concept can be thought of shrinking or expanding values.

Let’s take a simple case of  a 1*n and n*1  element matrix multiplication.

Analogy 1

In this analogy, ingredients are kept on a table as a row and recipe as column

[Ingredients][quantity] = [final product]

The output number can be thought of as the taste or quality of the final product. Although it is not a perfect analogy (eg. negative spoons are not possible in real life, – 2 spoons of sugar means nothing), the point here is we made a connection between abstract matrix multiplication process and a real life event and chances are rare that we forget both together.

Analogy 2

We can adjust the weights as we want is an additional insight here!. Isn’t this process looks like the features in machine learning or weights of a neural network ?

Creative unanswered questions on this topic

1. What is the need for such a row column rule ? Easy readability..?
2. Why don’t A*B != B*A..?

Conclusion

Let me wind up from the simple matrix multiplication concept. Matrix multiplication is related to Dot Product, so let’s explore more about it next!