Discussion
One way to interpret this theorem is that if the off-diagonal entries of a square matrix over the complex numbers have small norms, the eigenvalues of the matrix cannot be "far from" the diagonal entries of the matrix. Therefore, by reducing the norms of off-diagonal entries one can attempt to approximate the eigenvalues of the matrix. Of course, diagonal entries may change in the process of minimizing off-diagonal entries.
Read more about this topic: Gershgorin Circle Theorem
Famous quotes containing the word discussion:
“Power is action; the electoral principle is discussion. No political action is possible when discussion is permanently established.”
—Honoré De Balzac (1799–1850)
“Bigotry is the disease of ignorance, of morbid minds; enthusiasm of the free and buoyant. Education and free discussion are the antidotes of both.”
—Thomas Jefferson (1743–1826)
“Americans, unhappily, have the most remarkable ability to alchemize all bitter truths into an innocuous but piquant confection and to transform their moral contradictions, or public discussion of such contradictions, into a proud decoration, such as are given for heroism on the battle field.”
—James Baldwin (1924–1987)