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Prove that if is an eigenvalue of A with geometric multiplicity d, then is an eigenvalue
Chapter 6, Problem 9(choose chapter or problem)
QUESTION:
Prove that if is an eigenvalue of A with geometric multiplicity d, then is an eigenvalue of AT with geometric multiplicity d. (Hint: Use Theorem 4.6 of Chapter 3.)
Questions & Answers
QUESTION:
Prove that if is an eigenvalue of A with geometric multiplicity d, then is an eigenvalue of AT with geometric multiplicity d. (Hint: Use Theorem 4.6 of Chapter 3.)
ANSWER:Step 1 of 3
According to the definition, for any matrix having eigenvalue , the geometry multiplicity of is equal to the number of linearly independent eigenvectors of , which is same as the dimension of the null space of .