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

Spectral theorem for self-adjoint endomorphism

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

$\phi :V⟶V$

be a self-adjoint endomorphism.

Then there exists an

orthonormal basis of $V$ consisting of eigenvectors

of $\phi$.

Proof, Write another proof