Extension of scalars

So, let's say you have two things: some blocks (let's call them A blocks) and a basket (let's call it a B basket). The A blocks are all red, blue, green, or yellow, and the B basket is a light brown color.

You can take all the A blocks and put them in the B basket, and they will all look a little different because they are next to the brown color of the basket. For example, the yellow A block might look a little bit more orange-ish when it's in the brown basket, and the red A block might look a little bit more brown-ish.

Now, let's say the colors of the A blocks represent numbers. For example, let's say red is 1, blue is 2, green is 3, and yellow is 4. And let's say the basket represents a different way of looking at the numbers, like multiplying them by 2. So when you put the A blocks in the B basket, you are "extending" the meaning of the blocks to also include the way they look in this new context.

This is basically what "extension of scalars" means in math. You have some numbers, which could be represented by colors or anything else, and you "extend" their meaning to a new situation by multiplying them by a certain (usually) constant value. This can help you do math in different contexts and with different rules.