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Competitive Stats
Q48Section ST (Statistics (Q11–Q65))48 of 65

Eigenvalues of rotation matrices

Let O={P:P is a 3×3 real matrix satisfying PTP=I3 and det⁡(P)=1}\mathcal{O} = \{P : P \text{ is a } 3 \times 3 \text{ real matrix satisfying } P^T P = I_3 \text{ and } \det(P) = 1\}, where I3I_3 denotes the identity matrix of order 3. Then which of the following options is/are correct?

Multiple select: one or more options are correct. Select all of them, then submit — marks need the exact set.

Options

Select every correct option, then submit.