Orthogonalization

Orthogonalization is when you have a big group of things and want to make them all different from each other.

Think about a bunch of toys that you have in a basket. If you just throw them in there randomly, they might all get mixed up and it could be hard to tell which one is which. But if you take each toy and put them in a separate box, they will be organized and easy to find.

With orthogonalization, you are doing something similar with a group of numbers. You want to put them in separate boxes so that they don't get mixed up and it's easy to see which number is which.

To do this, you take the original group of numbers and find a way to make them all different from each other. You can do this by finding a new set of numbers that are "perpendicular" to the original numbers.

Imagine a sheet of graph paper with a bunch of dots on it. The dots are the original numbers. To make them all different, you draw lines that are perpendicular to each other, like a crossword puzzle.

Each line represents a new number that is different from all the other numbers. So now you have a bunch of boxes or lines that represent the original numbers, but they are all different and easy to tell apart.

This can be really helpful in math and science, because it makes it easier to work with large groups of numbers and keep track of everything.