Spectral theorem

The spectral theorem is a tool that helps mathematicians and scientists answer questions about certain kinds of equations. It is like a special kind of puzzle that can be solved using mathematical equations. With the spectral theorem, you are trying to figure out what solution will make an equation true. The equation you have to solve is called an eigenvalue equation and it looks like this: Ax=λx. This equation looks a bit confusing but it is actually quite simple. In this equation, A is a matrix (a special kind of table with a lot of numbers) and x and λ are numbers that you are trying to figure out. If you can figure out what numbers will make the equation true then you have solved the spectral theorem.