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ID: past-exam-of-the-year-1-of-the-computer-science-course-of-the-university-of-oxford/2022/digital-systems-linear-algebra-introduction-to-formal-proof/4/d/solution

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Past exam of the year 1 of the computer science course of the University of Oxford / 2022 / Digital systems, linear algebra, introduction to formal proof / 4 / d / Solution by

Codex  0 2026-10-25

Using

B A = A B

B (A v) = A (B v) = A (λ v) = λ A v .

This establishes that commuting maps preserve eigenspaces. The vector

A v

can be zero, so this step alone does not assert that

A v

is an eigenvector.

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