2.2 Convex Sets -- Examples

[@petere9383]

Was there a previous course? He began talking about probability distributions and I don't think I have heard that previously

[@andrewmeowmeow]

For copositive matrices exercise. Q1: intuitively, copositive matrices (M) are smaller (subspace) than PSD matrices (S) because x^TSx >= 0 for any x in R^n. But x^TMx >= 0 only for x in R^n_+. Q2: It is similar to the proof of PSD matrices are convex set. Hi Prof Caramanis, I am not familiar with the definition of "given support", and thus, I didn't finish the exercise for "the set of moments of distribution with given support". Could you explain the jargon "support on C" meaning in 6:46? Thanks!

[@constantine.caramanis]

By "moments with a given support" i mean that these are moments of a distribution, where the distribution only puts weight on the set C. So if C is the discrete points {-1,1}, then we are talking about the set of moments of distributions that put weight only on the two points -1 and 1.

[@andrewmeowmeow]

@@constantine.caramanis Thank you for your explanation!

[@mehmetfatihsahin9021]

Hi Prof Caramanis, do you plan to release any exercise sets to supplement this lecture series? Thanks!

[@constantine.caramanis]

I'd like to at some point, but no plans to do that in the very immediate future, unfortunately...

[@m2rahman]

Hi Prof Caramanis, in this video you defined the dot product as v1^T * M * v1. Is this based on a general formula of inner product of two matrices? thanks!

[@m2rahman]

Are you using, for two matrices A, B, = Trace(A^T * B) as the inner product formula? thanks

[@constantine.caramanis]

Yes, exactly. I am using the fact that the inner product of two matrices A and B of the same size is = \sum_{ij} A_ij B_ij, which also is equivalent to the trace formula you gave.

[@m2rahman]

@@constantine.caramanis thanks for clarifying! it makes sense.