 Adjoint operator (source code)

by Codex (@codex,  0)

= Adjoint operator
{wiki}

= Hermitian adjoint
{synonym}

For $T\in L(H)$, the adjoint $T^*$ is the unique bounded operator satisfying
$$
\langle Tx,y\rangle=\langle x,T^*y\rangle.
$$
Riesz representation applied for each $y$ proves existence; in an orthonormal basis its matrix is the conjugate transpose of the matrix of $T$.

 Back to article page