Hello. I have a linear operator, [tex]L[/tex], and its adjoint [tex]L^a[/tex]. [tex]L[/tex] is self-adjoint, so [tex]L=L^a[/tex]. I'm being told that the following is true: [tex]\langle f,Lh\rangle=\langle Lf,h\rangle[/tex]. But what if the scalar product is not the symmetric product? What if [tex]\langle f,h\rangle=\langle h,f\rangle^*[/tex] where [tex]^*[/tex] is complex conjugation ? Then my first equation tells me that [tex]\langle f,Lf\rangle=\langle Lf,f\rangle[/tex]. and the second one says that [tex]\langle f,Lf\rangle=\langle Lf,f\rangle^*[/tex]. But which is true?