Why is matrix multiplication defined the way it is?
When I first learned about it, the formula seemed too complicated and totally unintuitive! I wondered, why not just multiply elements at the same position together?
💡 Let me explain why! 💡
First, let's see how to even make sense of matrix multiplication!
The elements of the product are calculated by multiplying rows of 𝐴 with columns of 𝐵.
It is not trivial at all why this is the way. 🤔
To understand, let's talk about what matrices really are!
Matrices are actually just representations of 𝑙𝑖𝑛𝑒𝑎𝑟 𝑡𝑟𝑎𝑛𝑠𝑓𝑜𝑟𝑚𝑎𝑡𝑖𝑜𝑛𝑠: mappings between vector spaces that are interchangeable with linear operations.
Let's dig a bit deeper to see why are matrices and linear transformations are basically the same!