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

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

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# The rank of a block matrix as a function of the rank of its submatrice

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