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 Apr9 awarded Popular Question Mar30 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 Mar30 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. Mar29 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. Mar8 accepted When is the inverse of a sparse matrix dense? Feb12 asked When is the inverse of a sparse matrix dense? Feb4 comment Symmetric gram matrix and orthogonality By definition (for symmetric matrices) they are orthogonal if and only if $A^TA=I$. Feb1 revised There is relation that is symmetric and transitive but not reflexive? added 8 characters in body Feb1 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. Feb1 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. Feb1 answered There is relation that is symmetric and transitive but not reflexive? Dec25 comment Which of the following conditions must necessarily be true? You mean mutually exclusive conditions? Dec15 awarded Yearling Dec9 awarded Caucus Nov26 awarded Civic Duty Nov15 comment Is this polynomial irreducible in $\mathbb F_2[X]$ I agree. "Yes" is a solution to the above question. Nov15 comment Is this polynomial irreducible in $\mathbb F_2[X]$ wolframalpha.com/input/… Nov15 comment Is this polynomial irreducible in $\mathbb F_2[X]$ $$\left(x^8+x^5+x^4+x^3+1\right) \left(x^8+x^7+x^6+x^4+x^2+x+1\right)$$ Oct23 comment Find $x$ for which the rank is as minimal/maximal as possible Hint: The first and second rows are indepedent. So for all $x$, the rank is $\ge2$. There are only three rows, so the rank is $\le3$. There're not so many options... Oct19 answered How to show that the curve $(x,y,z) = \langle \cos t, \sin t, c\sin t\rangle$ is an ellipse?