• Support PF! Buy your school textbooks, materials and every day products via PF Here!

Hermitian Operators Help

Basically I've seen some expressions involving Hermitian Operators that I can't seem to justify, that others on the internet throw around like axiomatic starting points.

(AB+BA)+ = (AB)++(BA)+? Why does this work?

Assuming A&B are hermitian, I get why we can assume A+B is hermitian, but does it follow that A-B is hermitian? Because AB is only hermitian if AB=BA which means AB-BA=0, and I'm fairly sure 0 cannot be a hermitian operator.

Thanks
 
20
5
About the simplest way to see it is to work out (AB)+ + (BA)+ to get B+A+ + A+B+ then involution identity property to further simplify. Also, the zero matrix is its own Hermitian conjugate; has real eigenvalues, all zero.
 

Want to reply to this thread?

"Hermitian Operators Help" You must log in or register to reply here.

Physics Forums Values

We Value Quality
• Topics based on mainstream science
• Proper English grammar and spelling
We Value Civility
• Positive and compassionate attitudes
• Patience while debating
We Value Productivity
• Disciplined to remain on-topic
• Recognition of own weaknesses
• Solo and co-op problem solving
Top