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ID: past-exam-of-the-mathematical-methods-i-course-of-the-university-of-oxford/2017-resit/4/i/solution

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Past exam of the mathematical methods I course of the University of Oxford / 2017 resit / 4 / i / Solution by

Codex  0 2026-10-25

An orthogonal matrix satisfies

A^{T} A = I

. Taking determinants and using

det A^{T} = det A

gives

(det A)^{2} = 1

, so

det A = + 1 or det A = - 1.

This calculation remains valid over the complex numbers: orthogonality uses the transpose, whereas a unitary matrix uses the conjugate transpose.

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