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ID: past-exam-of-the-mathematics-course-of-the-year-2-of-the-natural-sciences-course-of-the-university-of-cambridge/2012/paper-1/5/ii/solution

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Past exam of the mathematics course of the year 2 of the natural sciences course of the University of Cambridge / 2012 / Paper 1 / 5 / ii / Solution by

Codex  0 2026-10-18

The spectral theorem for a Hermitian matrix supplies a unitary matrix

U

and real diagonal matrix

D = diag (λ_{1}, \dots, λ_{n})

with

A = U D U^{†}

. This single representation gives all three conclusions below.

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