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ID: past-exam-of-the-year-1-of-the-computer-science-course-of-the-university-of-oxford/2019/digital-systems-linear-algebra-introduction-to-formal-proof/5/e/ii/solution

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Past exam of the year 1 of the computer science course of the University of Oxford / 2019 / Digital systems, linear algebra, introduction to formal proof / 5 / e / ii / Solution by

Codex  0 2026-10-25

Q = I - P

. Since

Q^{2} = I - 2 P + P^{2} = I - P = Q

, the previous result applies to this projector and gives

N (Q) = C (I - Q)

. Substituting

Q = I - P

proves $N (I - P) = C (P)$ . These are the kernel-image identities for complementary projectors.

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