Spectral Theory of Compact Self Adjoint Operators
Israel Gohberg, Seymour Goldberg, M. A. Kaashoek · Birkhäuser Basel eBooks · 2003
One of the fundamental results in linear algebra is the spectral theorem which states that if H is a finite dimensional Hilbert 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 $$ A{{\varphi }_{i}} = {{\lambda }_{i}}{{\varphi }_{i}},1 \leqslant i \leqslant n. $$