?

Linear Algebra

Free Version

Upgrade subject to access all content

Moderate

Gershgorin

LINALG-KIZHLX

The Gershgorin set for an $n\times n$ complex matrix $A=(a_{ij})$ is a collection of disks in the complex plane centered at $a_{11},a_{22},\dots,a_{nn}$ which are guaranteed to contain all the eigenvalues of $A$.

If...

...is the Gershgorin set of a $5\times 5$ matrix $A$, we can say that:

A

$A$ is invertible

B

$A$ is singular (not invertible)

C

One cannot tell if $A$ is invertible or not