 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2014/paper-2/12/a/i/solution

Q

satisfies

Q^{T} Q = I,

equivalently

Q^{- 1} = Q^{T}

. Its columns, and also its rows, form an orthonormal basis. Consequently it preserves dot products and Euclidean norms.

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