Spectral theory

Spectral theory is a branch of mathematics that studies how things can be described by their shape or spectrum. Think of it like an abstract rainbow—each color of the rainbow is a different type of wave of light, and these waves together make up the rainbow. Spectral theory takes this idea and applies it to abstract equations, looking at how the spectrum of its solutions can describe the mathematical system. In simple terms, spectral theory is a way to understand things by looking at the pattern that its solutions form.