Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Obscure determinant question

  1. Aug 14, 2009 #1
    I'm working on some math that falls out of using a Kalman filter for estimation. I'd like to show that [tex]|G^T C_1^{-1} G + C_2^{-1}| \leq |G^T [diag(C_1)]^{-1} G + C_2^{-1}|[/tex] where [tex]C_1[/tex] and [tex]C_2[/tex] are covariance matrices and [tex]diag(C_1)[/tex] denotes the diagonal of matrix A.

    I've been able to show this is true when [tex]G=G^T=I[/tex] and [tex]C_2[/tex] is also diagonal. Numerical simulations suggest it is more generally true but I've been unable to convince myself of it on paper.
  2. jcsd
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?
Draft saved Draft deleted