Show that the set8. - {x = 87,Sa=X++S |Σlog (A, (X)) ≥ a},where a R and λ; (X) is the ith eigenvalue of X, is a convex set.(Hint: consider the function log det (X) we studied in class.)

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Answered: Show that the set Sa n { x = S² + [Ë…

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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Show that the set Sa n { x = S² + [Ë ¹0g (A, (X)) ≥ a}. = ++ log i=1 where a € R and λ; (X) is the ith eigenvalue of X, is a convex set. (Hint: consider the function log det (X) we studied in class.)