Hi everyone,(adsbygoogle = window.adsbygoogle || []).push({});

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

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# Vector spaces equation

Can you offer guidance or do you also need help?

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