I'm currently learning linear algebra, and I was confused by these two terminologies.
It seems that adjoint is the tranpose of cofactor matrix, and a self-adjoint operator has a matrix representation whose conjugate tranpose equal to itself.
But I just met a question, that ask me to prove
$$(im~L)^\perp=ker~L^*$$
where $L^*$ is the adjiont of L
It indicates that L*, the adjoint of L, is the conjugate transpose of L.
I wonder whether adjoint has something to do with self-adjoint.
If not, then what's their difference, and how do I tell the difference when digesting the description of any other question.
Thanks in advanced!