(a) (b) f(x) = ||XV||2 supveR"\{0} |v||2 on Rmxn f(x, y) = x¹Y-¹x on R" x S. '++
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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Question
a and b only
![Problem 4.
(a)
(b)
Show that the following functions are convex or concave:
||XV||2
f(X) = suPveR"\{0} |v||2
on Rmxn
f(x, y) = xTY-¹x on R" x S+
f(X) = (det (X))¹/m with dom f
= Sm
'++:
f(x) = (det (Ao + 1₁A₁ + ... + InAn))¹/m, on {x= [₁,..., In]¹ € R¹ | A0+₁A₁+
... +In An >0}, where A, E Sm.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F747ab200-c676-4ed9-b814-dae7641fcf0c%2F0bcc2501-d9c1-4ee1-a799-fec108fe2d44%2Fr49gdlv_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Problem 4.
(a)
(b)
Show that the following functions are convex or concave:
||XV||2
f(X) = suPveR"\{0} |v||2
on Rmxn
f(x, y) = xTY-¹x on R" x S+
f(X) = (det (X))¹/m with dom f
= Sm
'++:
f(x) = (det (Ao + 1₁A₁ + ... + InAn))¹/m, on {x= [₁,..., In]¹ € R¹ | A0+₁A₁+
... +In An >0}, where A, E Sm.
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