Gershgorin’s Circle Theorem

Question

why does Gershgorin’s Circle Theorem say that the eigenvalues of D are the diagonal elements of D?

D is a diagonal matrix with distinct real entries on the diagonal,

score 2 · Answer 1 · answered Mar 26 '14 at 03:39

2

The reason is that the sum of each row (not including the diagonal entry) is zero. Hence the Gershgorin disk has radius zero, i.e. is a single point.

answered Mar 26 '14 at 03:39

vadim123

1

And we might as well point out that the entries of $D$ do not need to be distinct or even real. – Andrés E. Caicedo Mar 26 '14 at 03:42
what do you mean "Gershgorin disk has radius zero, i.e. is a single point." – user2158735 Mar 26 '14 at 16:01
http://en.wikipedia.org/wiki/Gershgorin_circle_theorem – vadim123 Mar 26 '14 at 16:07

1 Answers1