Vector space/Inner product/Endomorphism/Self-adjoint/Definition

Self-adjoint endomorphism

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

$\phi :V⟶V$

be an endomorphism. Then $\phi$ is called self-adjoint if

$⟨\phi (u),v⟩=⟨u,\phi (v)⟩$

holds for all $u,v\in V$.