Overview
Given an operator
{% T:h \rightarrow H %}
on a
Hilbert Space {% H %}
that is both compact and self-adjoint then there exists a countable number of
nonzero real numbers {% \lambda_n %} (such that {% \lambda_n \rightarrow 0 %} for infinitely many {% \lambda_n %})
and an orthonormal basis {% e_n %} such that
{% Tx = \sum_n \lambda_n \langle x, e_n \rangle e_n %}
for any {% x \in H %}.