Let V be a finite-dimensional complex inner product space. For a linear map T: V → V, let T denote its adjoint. Which of the following statements is true?

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Mathematics · Linear Algebra

Verified Solution4 OptionsUpdated: October 2026👁️1 View

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Correct answer

Let v ∈ V be such that TT(v) = 0. Then T(v) = 0

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Answer 1

If TT = TT, then T must be an invertible operator.

Answer 2

If T = T, then T must be the zero operator.

Answer 3

Let v ∈ V be such that TT(v) = 0. Then T(v) = 0

Answer 4

If trace(TT) = 0, then T = 0

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