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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.)

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.)

Advanced Engineering Mathematics
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 8. - {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.)
Transcribed Image Text:Show that the set 8. - {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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