Vector space/Inner product/Endomorphism/Self-adjoint/Spectral theorem/Fact

Spectral theorem for self-adjoint endomorphism

Let ${}V$ be a ${}{\mathbb {K} }$-vector space, endowed with an inner product, and let

$\varphi \colon V\longrightarrow V$

be a self-adjoint endomorphism.

Then there exists an

orthonormal basis of ${}V$ consisting of eigenvectors

of ${}\varphi$.

Proof, Write another proof