# Why the spectral theorem is named “spectral theorem”?

"If $V$ is a complex inner product space and $T\in \mathcal{L}(V)$. Then $V$ has an orthonormal basis Consisting of eigenvectors of T if and only if $T$ is normal".

I know that the set of orthonormal vectors is called the "spectrum" and I guess that's where the name of the theorem. But what is the reason for naming it?

-
Rather: the set of eigenvalues of a linear map is what is called spectrum.In the spectral theorem, you decompose the linear map in (very simple!) pieces, each piece coming from one element of the spectrum. – Mariano Suárez-Alvarez Oct 22 '12 at 6:33
@Mariano, yes! My mistake, thanks. – Hiperion Oct 22 '12 at 6:36
I'm teaching a Linear Algebra course at the moment and if things go according to schedule, I'll be discussing the Spectral Theorem on Halloween's day. :) – Andrea Mori Oct 22 '12 at 10:36