- #1

GoodSpirit

- 18

- 0

Hello everyone,

I would like to post this problem here in this forum.

Having the following block matrix:

[tex]

\begin{equation}

M=\begin{bmatrix}

S_1 &C\\

C^T &S_2\\

\end{bmatrix}

\end{equation}

[/tex]

I would like to find the function $f$ that holds [tex]rank(M)=f( rank(S1), rank(S2))[/tex].

[tex]S_1[/tex] and [tex]S_2[/tex] are covariance matrices-> symmetric and positive semi-definite.

[tex]C[/tex] is the cross covariance that may be positive semi-definite.

Can you help me?

I sincerely thank you! :)

All the best

GoodSpirit

I would like to post this problem here in this forum.

Having the following block matrix:

[tex]

\begin{equation}

M=\begin{bmatrix}

S_1 &C\\

C^T &S_2\\

\end{bmatrix}

\end{equation}

[/tex]

I would like to find the function $f$ that holds [tex]rank(M)=f( rank(S1), rank(S2))[/tex].

[tex]S_1[/tex] and [tex]S_2[/tex] are covariance matrices-> symmetric and positive semi-definite.

[tex]C[/tex] is the cross covariance that may be positive semi-definite.

Can you help me?

I sincerely thank you! :)

All the best

GoodSpirit

Last edited: