Section 55: Problem 3 Solution
Working problems is a crucial part of learning mathematics. No one can learn topology merely by poring over the definitions, theorems, and examples that are worked out in the text. One must work part of it out for oneself. To provide that opportunity is the purpose of the exercises.
James R. Munkres
Show that if
is a nonsingular 3 by 3 matrix having nonnegative entries, then
has a positive real eigenvalue.
The proof is no different from Corollary 55.7 with the only difference in arguing why
.