Mathematics · Linear Algebra
Which of the following is correct about a diagonalizable operator T: V → V on a finite-dimensional vector space V?
Verified Solution4 OptionsUpdated: October 2026👁️1 View
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- 1The only diagonalizable operators are those with eigenvalues equal to 1.
- 2All eigenvalues of T must be distinct.
- 3The operator T is necessarily symmetric.
- 4The minimal polynomial of T splits into distinct linear factors.✓
Correct answer
The minimal polynomial of T splits into distinct linear factors.
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