We have the matrix $$A=\begin{pmatrix}2 & 0.4 & -0.1 & 0.3 \\ 0.3 & 3 & -0.1 & 0.2 \\ 0 & 0.7 & 3 & 1 \\ 0.2 & 0.1 & 0 & 4\end{pmatrix}$$ We get the row Gershgorin circles: $$K_1=\{z\in \mathbb{C} : |z-2|\leq 0.8 \} \\ K_2=\{z\in \mathbb{C} : |z-3|\leq 0.6 \} \\ K_3=\{z\in \mathbb{C} : |z-3|\leq 1.7 \} \\ K_4=\{z\in \mathbb{C} : |z-4|\leq 0.3 \} $$ and the column Gershgorin circles: $$K_1'=\{z\in \mathbb{C} : |z-2|\leq 0.5 \} \\ K_2'=\{z\in \mathbb{C} : |z-3|\leq 1.2 \} \\ K_3'=\{z\in \mathbb{C} : |z-3|\leq 0.2 \} \\ K_4'=\{z\in \mathbb{C} : |z-4|\leq 1.5 \} $$
To get the intervals of the eigenvalues, we have to look at the union of all row circles and the union of all column circles, or not?
Then at the result we have to take the intersection, or not?
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EDIT:
drawing the row disks we get the following, or not?
Do we get from that there are complex eigenvalues?
And the column disks:
right?