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Special Exercises (Chapter 0-3) Version: 15-09-2009
 

Summary: Special Exercises (Chapter 0-3)
Version: 15-09-2009
Ex.1.6 Given the quadratic function on Rn,
f(x) = xT
Qx + cT
x + d,
with symmetric matrix Q, c Rn, d R. Show (by only
using the def. of convexity) that f is convex iff Q is psd.
Ex. 1.15' Show that for S Rn the set aff (S) is the smallest
affine space containing S.
Recall that the affine hull of the set S is defined by:
aff (S) = {x | x =
k
i=1
ixi
, xi
S, i R,
k
i=1
i = 1, k 1}

  

Source: Al Hanbali, Ahmad - Department of Applied Mathematics, Universiteit Twente

 

Collections: Engineering