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

Block of a covariance matrix

  1. Feb 4, 2013 #1
    Hello everybody,

    I’d like to present this math problem that I’ve trying to solve…
    This matter is important because the covariance matrix is widely use and this leads to new interpretations of the cross covariance matrices.
    Considering the following covariance block matrix :
    [tex]
    \begin{equation}
    M=\begin{bmatrix}
    S1 &C \\
    C^T &S2 \\
    \end{bmatrix}
    \end{equation}
    [/tex]

    The matrix S1 and S2 are symmetric and positive semi-definite.C is also positive semi-definite
    What I am trying figure out is :
    1- I would like to discover the relation between the eigenvector of M and the eigen vectors of S1 and S2.
    2- Discover the relation between the eigenvector of the matricez S1,S2 and C.
    I used the eigendecomposition but it lead to a very complicated expressions…
    Could you help me suggesting another approach?

    I really thank you!

    All the best

    GoodSpirit
     
  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?
Draft saved Draft deleted



Similar Discussions: Block of a covariance matrix
  1. Covariance Matrix (Replies: 7)

Loading...