Mathematics · Linear Algebra
Let T: ℂn → ℂn be a ℂ-linear operator with distinct eigenvalues 2, 3, and 5. Suppose (T - 2I)2(T - 3I)2(T - 5I)2 = 0. Which of the following statements is necessarily true?
Verified Solution4 OptionsUpdated: October 2026👁️1 View
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- 1(T - 2I)(T - 3I) is a nilpotent operator.
- 2The minimal polynomial of T must degree 6.
- 3T is diagonalizable over ℂ in all cases.
- 4T has at least three linearly independent eigenvectors.✓
Correct answer
T has at least three linearly independent eigenvectors.
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