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

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- Solution d

Solution

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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