Scalar multiplication

Scalar multiplication is when you take a number and make it bigger or smaller, but also change the direction it points in. Imagine you have a toy car and you want to move it forwards. You could push it with your hand and it will move straight in front of you. But if you want to move it faster, you can push it harder and it will go further. This is kind of like scalar multiplication.

In math, we use numbers instead of pushing things with our hands. Let's say we have a line with two points on it, point A and point B. We want to move from point A to point B, but we want to go twice as fast. We can do this with scalar multiplication. We start at point A and then we multiply the distance between A and B by 2. This means we are moving twice as fast as before. But we also change direction - instead of moving towards point B, we move in the opposite direction. This might sound weird, but imagine you are walking backwards twice as fast as you normally would. You would still be moving away from where you started, but you would be doing it faster.

We can also use scalar multiplication to move in the opposite direction. Let's say we want to move from point A to point B, but we want to go backwards. We can do this by multiplying the distance between A and B by -1. This means we are moving in the opposite direction. This might sound confusing, but imagine you turn around and walk the same distance as before, but in the opposite direction. You would end up back where you started.

So scalar multiplication is kind of like pushing a toy car, but we use numbers to make things go faster or slower, and we also change direction when we do it.