I need to compute the inverse of the following sum of matrices:
$$\begin{pmatrix} 0 & B \\ B^T & 0 \end{pmatrix} +D $$
where B is a non-negative matrix and D is a non-negative diagonal matrix. They are both real an square matrices.
Asked
Active
Viewed 68 times
0
-
Why do you think the inverse exists ? – TheSilverDoe Oct 20 '20 at 17:20
1 Answers
0
By definition, non-negative matrices are those matrices with non-negative entries. Suppose, $\begin{pmatrix} 0&2\\2&0\end{pmatrix}=\begin{pmatrix} 0&B\\B^{T}&0\end{pmatrix}$ and $D=\begin{pmatrix} 2&0\\0&2\end{pmatrix}$. Then the inverse of the sum of matrices doesn't exist.
Cherryblossoms
- 917
-
-
Can you please explain the point? Because, I only followed the statement of your question. – Cherryblossoms Oct 21 '20 at 02:33
-
I simply wanted to ask if any of you is aware of a properties that allows me to easily compute IN GENERAL the inverse of the sum of two matrices, where one is diagonal D and the other one is a symmetric anti-diagonal matrix (as written above). I'm not interested in the specific cases where the inverse does not exist. But I guess I wrote the post in a sloppy way, and I am sorry for that – Sebastiano Della Lena Oct 21 '20 at 12:18