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Jul
2
awarded  Curious
Nov
14
awarded  Teacher
Nov
14
comment Exclude an RGB color from a set
This is probably best asked in a Machine Learning group, I would suggest trying the stats stack exchange site. What you're looking for is a clustering algorithm, to accept the data points that are close together in your space, and reject outliers. This can be a tricky problem, and the stats people will have a much better background for answering your question than just pure mathematics.
Nov
14
answered Water tank problem
Nov
14
asked Product of positive definite matrices not itself positive definite
May
17
comment Derivative of conjugate transpose of matrix
You've worked hard for this acceptance, thank you for your effort!
May
17
accepted Derivative of conjugate transpose of matrix
May
16
awarded  Commentator
May
16
comment Derivative of conjugate transpose of matrix
This seems like it's kind of cheating though..... :P I see you've gotten the "correct" answer, but modifying an entry in $W$ will certainly modify it in $W^H$ and vice versa, therefore I don't see how we can ignore one or the other as a "constant"
May
16
asked Derivative of conjugate transpose of matrix
May
14
comment Solving for a matrix from its quadratic form
I get it! Thank you so much!
May
14
accepted Solving for a matrix from its quadratic form
May
14
comment Solving for a matrix from its quadratic form
Also, because the $vec(Z)$ operation transforms from a matrix to a vector, must we still use the Frobenius norm notation $\| \cdot \|_F$? It should be functionally equivalent to the $\ell^2$ norm again, right?
May
14
comment Solving for a matrix from its quadratic form
Excellent. This is exactly what I needed. I had apriori knowledge that $W = YX^H (X X^H)^{-1}$ but I could not figure out how to get there from the problem statement. I don't fully understand your answer, so I'd like to ask some questions. I understand your expansion with Kronecker products and such, but I don't understand how you isolate $vec(W)$ on the left hand side. I get the last conversion from Kronecker products back to plain matrix multiplication, but I have a hard time pulling things apart in my head for the step before that. Can you help me work that out?
May
14
comment Solving for a matrix from its quadratic form
This is a good insight. I'm going to go think about it! If I decide that I need help with this new formulation, should I open a new question, or edit this one appropriately? And thank you for your help!
May
14
comment Solving for a matrix from its quadratic form
An excellent point. I have updated my answer to explain why this question is slightly better posed. Essentially, I have multiple $x$ and $y$ vectors that I can bring in to help narrow the problem down.
May
14
revised Solving for a matrix from its quadratic form
Explained that I have multiple sets of vectors, therefore the W matrix is not as underdetermined as previously thought
May
14
asked Solving for a matrix from its quadratic form
Mar
3
awarded  Supporter
Jan
20
awarded  Editor