 Solution

ID: past-exam-of-the-numerical-linear-algebra-and-approximation-course-of-the-university-of-oxford/2008/1/a/i/solution

Q

satisfies

Q^{T} Q = Q Q^{T} = I

. Equivalently its columns form an orthonormal basis. In particular it preserves the Euclidean norm, since

∥ Q x ∥_{2}^{2} = x^{T} Q^{T} Q x = ∥ x ∥_{2}^{2}

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