By Bettina Hoser
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Additional info for Analysis of Asymmetric Communication Patterns in Computer Mediated Communication Environments
But all these three are based on the role a member holds in a given community. In the context of this book these abstract concepts will be used to describe results of mathematical evaluation with respect to the communication behavior of a member of the group. The following view is adopted: a member can have different roles, for example anchor or lurker (see later for a detailed explanation). The role has an inherent rank or status and at the same time an inherent prestige. Both depend on the mathematical computation defined on the communication traffic generated by each member.
2 it also yields an additional interpretation in the context of communication pattern analysis. 6 Perturbation Theory for Hermitian Operators The behavior under perturbation is well researched for Hermitian operators [Kat95], [DS88] . And since this is a major advantage of the proposed method when thinking of future work in this field, a very short introduction at least for perturbation of eigenvalues is given. ✗ ✒ ✒ with eigenvalues ❑ ❢ ➛❁➛❁➛ Now assume aná unperturbed Hermitian matrix á ✔ ❑ ❜ , with ❑ ❢ ➛❁➛❁➛ ❑ ❜ and a Hermitian perturbation matrix with eigenvalues ❢⑨ ✒ ➛❁➛❁➛ ✒ ⑨ ❜ , with ⑨ ❢ á ➛❁➛❁➛ á ⑨ ❜ .
Be any complex number ✄✆☎✞✝ ❅→ï❃✜❵❫➸➵ with absolute value ï 2. 1) ✄❯✝÷☎ ❅→● ✄❯☎➟✝ ❅➘●❱ï✑✜✑✾❯❫➸➵ 3. ✄❯☎➟☎ ❅➐✳✙❅➐Ñ ☎✞☎ because of the exclusion of self references 4. After rotation about ❇ : Ñ ✞☎ ✝ ❅ 5. Ñ ÷✝ ☎ ❅ ✄✆☎✞✝ ✜❵❫✽❈◆❅→ï✑✜❵❫➸➵➫✜❵❫✽❈◆❅→ï✑✜❵❫❐❽❡➵ ❋ ❿ ✆✄ ✝÷☎ ✜❵❫✽❈✖❅➘●✸ï❃✜✑✾❯❫❸➵✑✜❵❫✘❈✖❅➐✜ ❫❃❂ ï❃✜❵❫❐❉❽ ❈➩✾✺➵ ❮ ➟☎ ✝ 6. For Hermitian ❿ matrices Ñ ❅ ï❃✜✑✾❯❫❐❽❁❂ ❮ ❋ ❈✺✾✺➵ . 20), therefore, ï✑✜❵❫❐❽❸➵ ❋ ❿ ❈ ❅ 44 CHAPTER 4 7. This holds, if ✿ ➶ ➑ ➶ ❇ ❅❨❦ ➧ ❦❊❇ ➑ . ✥ ✿ 8. Solving for ❇ leads to ❊✢❇⑦❅❈❦ ➧ .
Analysis of Asymmetric Communication Patterns in Computer Mediated Communication Environments by Bettina Hoser