Spectral Theory of Compact Self Adjoint Operators

Abstract

One of the fundamental results in linear algebra is the spectral theorem which states that if H is a finite dimensional Hubert space and A ∈ L(H) is self adjoint, then there exists an orthonormal basis φ₁,…, φ_n for H and real numbers λ₁,…, λ_n such that

$$ A{\varphi _i} = {\lambda _i}{\varphi _i},\quad l \leqslant i \leqslant n $$

.