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wu :: forums    riddles    putnam exam (pure math) (Moderators: SMQ, Eigenray, towr, Icarus, Grimbal, william wu)    Decomposing Projection Operators « Previous topic | Next topic » Pages: 1  Reply Notify of replies Send Topic Print    Author  Topic: Decomposing Projection Operators  (Read 789 times) JocK Uberpuzzler     Gender: Posts: 877 Decomposing Projection Operators   « on: Jan 28th, 2006, 6:25am » Quote Modify Consider two non-commuting projection operators P and Q on a finite-dimensional inner-product space (i.e. two operators which are idempotent P2 = P, Q2 = Q and for which PQ =/= QP). Prove that it is not possible to construct non-negative operators R00, R01, R10, R11 (i.e. Hermitean operator with non-negative eigenvalues) such that:   R00 + R01 = P   R10 + R11 = I - P   R00 + R10 = Q   R01 + R11 = I - Q   (I is the identity operator).   « Last Edit: Jan 28th, 2006, 6:43am by JocK » IP Logged solving abstract problems is like sex: it may occasionally have some practical use, but that is not why we do it. xy - y = x5 - y4 - y3 = 20; x>0, y>0. Pages: 1  Reply Notify of replies Send Topic Print Forum Jump: ----------------------------- riddles -----------------------------  - easy   - medium   - hard   - what am i   - what happened   - microsoft   - cs => putnam exam (pure math)   - suggestions, help, and FAQ   - general problem-solving / chatting / whatever ----------------------------- general -----------------------------  - guestbook   - truth   - complex analysis   - wanted   - psychology   - chinese « Previous topic | Next topic »

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