Let V be a finite dimensional vector space over C and let T be a linear operator on V.Suppose there exist non-zero vectors a and 3 in V such thatT(a) ciß, T(B) = c₂a.Prove that √cic2 or √c1c2 is an eigenvalue of T.-

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Answered: Let V be a finite dimensional vector…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Let V be a finite dimensional vector space over C and let T be a linear operator on V. Suppose there exist non-zero vectors a and 3 in V such that T(a) cß, T(B) = c₂a. Prove that √cic2 or √c1c2 is an eigenvalue of T.