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!
If you are building a product, chances are you severely underestimate the importance of idea validation. (Especially if you are a developer.)
Key business assumptions can flop because you fail to look at different angles.
What are some basic questions to ask?
🧵 A thread. 🧵
𝐀𝐦 𝐈 𝐬𝐨𝐥𝐯𝐢𝐧𝐠 𝐚𝐧 𝐞𝐱𝐢𝐬𝐭𝐢𝐧𝐠 𝐩𝐫𝐨𝐛𝐥𝐞𝐦?
Often, the problem is not important enough to justify the existence of a solution. This is the most basic trap to fall for: there is no market need for the product.
Take a look at the top 20 reasons why startups fail by @CBinsights. The number 1 is no market need, causing around 43% percent of failures.