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Jun
7
comment Prove properties of $e^A$ when $A$ is a matrix
The second statement, as it stands, is wrong. As a counterexample, take $A$ to be the zero matrix.
May
20
accepted A maximization problem within the simplex
May
14
comment Is it always true that the complement of a closed set is open?
This reminds me of my lecturer in General Topology. He was quite an ambiguous fellow, and was rarely clear or precise about what he said. When introducing the concept of an open/closed set he told us "The door parable", which was: "A set is like a door. It can be either open, or closed. Except that a set can also be neither. Oh, and also both. You know what, forget about it..."
May
5
comment A maximization problem within the simplex
@copper.hat Yup. You're right. How didn't I think of that? You want to post an answer?
May
5
asked A maximization problem within the simplex
Apr
9
awarded  Popular Question
Mar
30
comment Linear regression of time series data - moving linear regression
I don't know if this can be done in a simple way, but as a start I'd note that least-square fitting is done by calculating the inverse of a matrix of the form $A^TA$ where $A$ is a matrix constructed from the observations. Updating the inverse in each incremental step might be done via the Sherman-Morrison formula
Mar
30
comment Linear regression of time series data - moving linear regression
Why not use weights, that decrease (say, exponentially), the further you go into the past? That is, use a standard linear regression with weights $w_i=e^{-\lambda i}$ where $w_i$ is the weight of the $i$-th measurement, and the most recent measurement is $i=1$. $\lambda$ is a parameter that determines how much you want to bias your estimate towards more recent data.
Mar
29
comment Minimal distance between points on two graphs
Nice question. I don't have time to solve it now, but I think that defining the distance function as $$f(x,y)=(x-y)^2+(\sin(x)+2-\sin(y))^2$$ and moving to the variables $$x'=x-y,\qquad y'=x+y$$ might greatly simplify things.
Mar
8
accepted When is the inverse of a sparse matrix dense?
Feb
12
asked When is the inverse of a sparse matrix dense?
Feb
4
comment Symmetric gram matrix and orthogonality
By definition (for symmetric matrices) they are orthogonal if and only if $A^TA=I$.
Feb
1
revised There is relation that is symmetric and transitive but not reflexive?
added 8 characters in body
Feb
1
comment There is relation that is symmetric and transitive but not reflexive?
OK. I still think it's a matter of taste, but I'll edit my answer.
Feb
1
comment There is relation that is symmetric and transitive but not reflexive?
That's a matter of taste. If you assume that $y$ exists and that $y=x$ then it's like assuming reflexivity in the first place, which is kind of cheating.
Feb
1
answered There is relation that is symmetric and transitive but not reflexive?
Dec
25
comment Which of the following conditions must necessarily be true?
You mean mutually exclusive conditions?
Dec
15
awarded  Yearling
Dec
9
awarded  Caucus
Nov
26
awarded  Civic Duty