Solution Found!
Prove or give a counterexample: If A and B have the same characteristic polynomial, then
Chapter 6, Problem 8(choose chapter or problem)
QUESTION:
Prove or give a counterexample: If A and B have the same characteristic polynomial, then A and B are similar.
Questions & Answers
QUESTION:
Prove or give a counterexample: If A and B have the same characteristic polynomial, then A and B are similar.
ANSWER:Step 1 of 2
Consider A and B as the two matrices of order n where A is non -singular matrix. Then,
The above expression suggest that AB and BA are similar. Thus, both have same characteristics polynomial, eigenvalues and multiplicities.