Exercise 5.2.9

Answers

1.

Because the characteristic polynomial of

T

is independent of the choice of

β

, we know that the characteristic polynomial

f (t) = \det ({[T]}_{β} - tI) = \prod_{i = 1}^{n} ({({[T]}_{β})}_{ii} - t)

splits, where the second equality holds since it’s a upper triangular matrix.

2.

The characteristic polynomial of a matrix is also the same for all matrices which is similar to the original matrix.

jephianlin

2011-06-27 00:00