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3.18 Adapt the proof of concavity of the log-determinant function in §3.1.5 to show the follow- ing. (a) f(X) = tr (x-') is convex on dom f = S+. (b) f(X) = (det X)/" is concave on dom f = S,+: 1/n

3.18 Adapt the proof of concavity of the log-determinant function in §3.1.5 to show the follow- ing. (a) f(X) = tr (x-') is convex on dom f = S+. (b) f(X) = (det X)/" is concave on dom f = S,+: 1/n

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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3.18 Adapt the proof of concavity of the log-determinant function in §3.1.5 to show the follow- ing. (a) f(X)= tr (x-') is convex on dom f = S+. (b) ƒ(X) = (det X)/" is concave on dom f = S,+: 1/n
Transcribed Image Text:3.18 Adapt the proof of concavity of the log-determinant function in §3.1.5 to show the follow- ing. (a) f(X)= tr (x-') is convex on dom f = S+. (b) ƒ(X) = (det X)/" is concave on dom f = S,+: 1/n
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