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Vector spaces equation

  1. Aug 2, 2013 #1
    Hi everyone,

    I would like to ask you something about vector spaces.
    I have the following term:

    [tex]
    S=dim(R(
    \begin{bmatrix}
    \Sigma_{x1}\\
    CC^{T}\\
    \end{bmatrix}
    \phi_1) \cap R(
    \begin{bmatrix}
    CC\\
    \Sigma_{x2} \\
    \end{bmatrix}
    \phi_2) )
    [/tex]

    where

    [tex]
    \Sigma_{x1} \in \mathbb{R}^{nxn} \\
    \Sigma_{x2} \in \mathbb{R}^{nxn}\\
    CC \in \mathbb{R}^{nxn}\\
    \phi_1 \in \mathbb{R}^{l1xn}\\
    \phi_2 \in \mathbb{R}^{l2xn}\\
    [/tex]

    and

    [tex]
    rk(\Sigma_{x1})=s1\\
    rk(\Sigma_{x2})=s2
    [/tex]

    [tex]
    R(X)
    [/tex] is the column space (range) defined by the columns of the matrix X.

    My goal is to express S in terms of s1, s2, l1 and l2.
    I really thank you for your help.

    All the best

    Ricardo Sousa
     
  2. jcsd
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