Mathematics · Linear Algebra
Let S, T: C2 → C2 be C-linear transformations and I denote the identity transformation on C2. Which of the following statements is necessarily true?
Verified Solution4 OptionsUpdated: October 2026👁️1 View
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- 1(ST - TS)2 = λI for some λ ∈ C
- 2The characteristic polynomial of (ST - TS)2 is (x - λ)2 for some λ ∈ C✓
- 3If S and T have a common eigenvector, then ST - TS = λI for some λ ∈ C
- 4If ST - TS has only one eigenvalue, then (ST - TS)2 is the zero transformation
Correct answer
The characteristic polynomial of (ST - TS)2 is (x - λ)2 for some λ ∈ C
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