Unitary matrix

A unitary matrix is like a special kind of calculator that makes numbers do special things. These calculators have a special property where they can take a number and change it in a certain way without changing certain important things about it, like its length or angle.

Think of a big piece of paper with an arrow drawn on it. The length of the arrow is important because it tells us how "big" the number is. The angle of the arrow is important because it tells us the direction of the number. A unitary matrix is like a special tool that can take the whole paper with the arrow and change it in a special way, without changing the length or angle of the arrow.

For example, a unitary matrix might take the paper and flip it around or rotate it in a special way, but the arrow stays just as long and still points in the same direction. This is useful because sometimes we need to change the orientation of numbers in a way that doesn't mess up the important things about them.

So, to sum up: a unitary matrix is like a special calculator that can change the orientation of numbers in a way that doesn't change their length or angle, which is very useful in lots of math problems.