Luboš Motl
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 Jun 10 awarded Nice Answer Jun 10 answered Finding power series representation of $\int_0^{\frac{\pi }{2}} \frac{1}{\sqrt {1 - k^2\sin^2{x}}}\;{dx}$ Jun 9 comment A radius for which the inverse of a function is well defined (Inverse Function Theorem) The four derivatives $\partial f_{1,2} / \partial (x,y)$ are all nonzero at $(1/2,0)$ and the matrix is non-singular over there, so it's clear that in a vicinity of the point, the inverse exists. Jun 9 comment A radius for which the inverse of a function is well defined (Inverse Function Theorem) Maybe they just want an approximate formula for the inverse? I can't imagine how the formulae could simplify. Or maybe you're allowed to use some symbols inside? Something that makes the solution "non-explicit"? Jun 9 answered Question about direct sum of function space Jun 9 answered A radius for which the inverse of a function is well defined (Inverse Function Theorem) Jun 9 comment A radius for which the inverse of a function is well defined (Inverse Function Theorem) I see, thanks, it's a comma. ;-) Jun 9 comment A radius for which the inverse of a function is well defined (Inverse Function Theorem) Sorry, I may be missing something, but how can you invert a function of two variables? Your function is from $R^2$ to $R$, so it cannot be a simple function, so it can't be (fully) inverted. The inverse function would have to be from $R$ to $R^2$, right? Jun 9 comment Finding number of matrices whose square is the identity matrix Hi, every $9\times 9$ matrix $A$ may be brought into the standard form $A=CDC^{-1}$ for a $D$ which is either diagonal or has the Jordan blocks on the diagonal. That's a basic result in algebra. In this form, $A^2 = CDC^{-1}CDC^{-1} = CD^2 C^{-1}$. It should be equal to $I = CC^{-1}$ which implies $D^2=I$. So $D$ has to have $\pm 1$ eigenvalue and one may check that the nondiagonal Jordan blocks would fail to produce $D^2=1$, too. Jun 9 revised Finding number of matrices whose square is the identity matrix added 263 characters in body Jun 9 answered Finding number of matrices whose square is the identity matrix Jun 8 answered What's the value of $\sum\limits_{k=1}^{\infty}\frac{k^2}{k!}$? Jun 6 revised Bounding ${(2d-1)n-1\choose n-1}$ added 199 characters in body Jun 6 revised Bounding ${(2d-1)n-1\choose n-1}$ added 560 characters in body Jun 6 answered Bounding ${(2d-1)n-1\choose n-1}$ Jun 6 revised Minimum value of $x+4z$ subject to the constraint $x^2+y^2+z^2\leq 2$? added 59 characters in body Jun 6 answered Minimum value of $x+4z$ subject to the constraint $x^2+y^2+z^2\leq 2$? Jun 6 comment Minimum value of $x+4z$ subject to the constraint $x^2+y^2+z^2\leq 2$? You switch $1$ and $3$ in $F$ which is from $R^3$ to $R$, not the other way around. Jun 6 answered Questions about open sets in ${\mathbb R}$ Jun 5 comment Piecewise smooth, non-orientable, closed-surface: a contradiction in terms, or am I going mad? Dear @Tom, it was a pleasure. The Möbius strip is nothing else than a properly chosen one half of the Klein Bottle. Place a topologically nontrivial circle in the Klein bottle - for example, run from the bottom of the bottle along the throat to the left, and return to the same place. And then cut it along this circle by scissors. You will get an unorientable surface with one boundary - the circle - and it's the Mobius strip. It's safer to cut a strip along the circle I just mentioned, this one is manifestly a Mobius strip. Unlike the Klein bottle, the Mobius strip has a boundary.