Exercise 5.2.6

Answers

1.
An operator T is diagonalizable ensure that its characteristic polynomial splits by Theorem 5.6. And in this situation Theorem 5.9(a) ensure that the multiplicity of each eigenvalue meets the dimension of the corresponding eigenspace. Conversly, if the characteristic polynomial splits and the multiplicity meets the dimension, then the operator will be diagonalizable by Theorem 5.9(a).
2.
Replace T by A again.
User profile picture
2011-06-27 00:00
Comments