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

Linear Operators

  • Thread starter blanik
  • Start date
I'm not sure where to start with these proofs. Any suggestions getting started would be appreciated.

1. Show that is A,B are linear operators on a complex vector space V, then their product (or composite) C := AB is also a linear operator on V.

2. Prove the following commutator relationships for Linear Operators A,B,C:
a. [A,B + C] = [A,B] + [A,C]
b. [A,B] = -[B,A]
c. [A,BC] = B[A,C] + [A,B]C
d. [AB,C] = A[B,C] + [A,C]B


Staff Emeritus
Science Advisor
Gold Member

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

Hot Threads