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!

Schur complement question

  1. Apr 8, 2010 #1
    Let M be a real symmetric and positive definite matrix with blocks A, Bt, B and C.


    [tex] M= [[A,B^{t}] ; [B,C]] [/tex]

    where [tex] A[/tex] is a [tex] p\times p[/tex] matrix;[tex] B[/tex] is [tex] q\times p[/tex]; and [tex] C[/tex] is [tex] q\times q[/tex].

    Let [tex] S=C-BA^{-1}B^{t}[/tex] be the Schur complement. We prove that S is symmetric positive definite.


    I can prove that S is symmetric but I am having trouble proving that it is positive definite.
    I know that for S a symmetric matrix, S positive definite is equivalent to say that all eigen values of S are positive.

    I guess my question is how do we prove that all eigen values of S are positive?
     
  2. jcsd
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?



Similar Discussions: Schur complement question
  1. Curvature Questions, (Replies: 0)

  2. Derivation question (Replies: 0)

  3. Topology question (Replies: 0)

  4. Flux question (Replies: 0)

  5. Question on Galois (Replies: 0)

Loading...