1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Hermitian Inner Product

  1. Mar 11, 2006 #1
    I'm getting some confusing information from different sources. If an inner product satisfies conjugate symmetry, it is called Hermitian. But the definition of a hermitian inner product says it must be antilinear in the second slot only. Doesn't conjugate symmetry imply that it's antilinear in both slots?
     
    Last edited: Mar 11, 2006
  2. jcsd
  3. Mar 11, 2006 #2

    AKG

    User Avatar
    Science Advisor
    Homework Helper

    Conjugate symmetry (plus linearity in the first slot) implies antilinearity in the second:

    [tex]\langle u,\,\alpha v\rangle = \overline{\langle \alpha v,\, u\rangle } = \overline{\alpha \langle v,\, u\rangle } = \overline{\alpha}\overline{\langle v,\, u\rangle } = \overline{\alpha}\langle u,\, v\rangle[/tex]

    If you think conjugate symmetry implies antilinearity in both, present a proof for it.
     
  4. Mar 11, 2006 #3
    I thought conjugate symmetry and antilinearity in the second slot implied antilinearity in the first, but I made an error when pulling out the constant.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Hermitian Inner Product
  1. Inner product (Replies: 2)

  2. Inner product (Replies: 2)

  3. Inner Product (Replies: 10)

  4. Inner Products? (Replies: 7)

Loading...