Question

What is self adjoint? Please give examples.

Answer 1

I assume you're talking about matrices. A matrix M is self adjoint if it is equal to its transpose
\[M = M^T\]

Notice that this means first of all that M must be a square matrix.

It's easy now to construct examples, take for example M to be a 2x2 matrix, then an example of a self-adjoint M is ...

Answer 2

\[\text{In a Hilbert space $H$, the adjoint of a linear opeator $T$ is a linear operator $T^*$ such that}\]\[\langle Tx, y\rangle = \langle x, T^*y\rangle \quad \forall x, y\in H.\]\[\text{An operator $T$ is self-adjoint if its adjoint is $T$ itself, that is $T^* = T$.}\]\[\text{For example, in the Hilbert space $H = \mathbb{R}^n$, any symmetric matrix is self-adjoint.}\]

Answer 3

@Krebante: ha, yes. I am assuming though from the question that we're not functional analysis. :-)

Answer 4

I'm doing quantum mechanics at the moment :)

Answer 5

Then Hilbert spaces it is, my apologies.

Answer 6

Nothing to apologize for, my mistake for not saying that :)