Beni Bogosel
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 2d comment inverse of sum of diagonal matrix and eigendecomposition I don't think that you can compute the inverse of a sum, in terms of the inverses of the two matrices. Apr12 comment Set of points at which a function coincides with its convexification is compact? Yes, I guess lower semicontinuous could work. Apr12 comment $x\over(1-x)$ $y\over(1-y)$ $z\over(1-z)$ >= 8 when $x ,y ,z$ are positive proper fractions and $x+y+z = 2$ What does proper fractions mean? Are they rational numbers? Apr11 comment Proving properties about matrix $A$ s.t. $A^2 = -I$ The equation you get for $\lambda$ is $\lambda^2 = -1$. This has roots $\pm i$. The sum of the eigenvalues is equal to the trace (the sum of the elements on the diagonal), and since $A$ has real entries, the trace is real. Apr11 comment For $n \ge 3$, every subgroup of $A_n$ with index $n$, is isomorphic to $A_{n-1}$ I guess you could use the fact that for $n \geq 5$, normal subgroups of $S_n$ are $\{e\},A_n,S_n$. Prove that a subgroup of $A_n$ with index $n$ is a normal subgroup of a group isomorphic to $S_{n-1}$. Then its cardinality implies that it can only be $A_{n-1}$. Apr10 comment Learning modern differential geometry before curves and surfaces I don't see why what you are doing could not be "safe". But it's just like talking about derivatives, without actually finding a derivative of a concrete function like $\exp,\sin,\ln$. Differential geometry was not a success for me, and as I look back, is this lack of concrete examples and connection with the curves and surfaces which kept me from learning more. I liked this course on curves and surfaces: alpha.math.uga.edu/~shifrin/ShifrinDiffGeo.pdf If you like differential geometry, you'll like curves and surfaces. Apr10 comment Learning modern differential geometry before curves and surfaces If you're comfortable with geometry on manifolds, it costs nothing to take a look into curves and surfaces. How can you speak of the tangent space to a manifold without being able to work with tangents to curves, or tangent planes to surfaces? How do you compute the curvature of a curve, or the mean curvature of a surface at a point? These are basic questions you need to know from curves and surfaces... Apr9 comment Please help solve for the variables A and B Replace B in the first equation. Then you'll have just an equation in A Apr9 comment Find all functions $f$ such that if $a+b$ is a square, then $f(a)+f(b)$ is a square @Elaqqad: The article you cite proves this only for polynomials, as far as I see. Apr9 comment Unique solution of nolinear equation set Yes, that's true. Apr9 comment Find all functions $f$ such that if $a+b$ is a square, then $f(a)+f(b)$ is a square Does $\Bbb{N}^+$ contain zero? Apr9 comment Symmetric matrix with zero elements below the anti-diagonal Note that doing two line swaps (i.e. multiplication with a permutation matrix) this turns into a lower triangular matrix. Apr8 comment Convergence of Cesàro means for a monotonic sequence @thomas Why not? Since $a_n$ is monotone, if it diverges, it must have a limit equal to $\pm \infty$. Then the chain of the inequalities says that the middle partial limits must both be equal to the same infinite limit. This contradicts the hypothesis on the convergence of the mean. Apr8 comment Proving summations involving the Legendre symbol Are those quadratic residues? Apr8 comment A sequence for which there is $k$ such that for each $\epsilon >0$ we have that $|x_n -l | < \epsilon$ for all $n \geq k$ Yes, that's the conclusion. Apr8 comment Let $f: [0,\infty] \to \mathbb{R}$ be continuous such that its limit tends to $0$ as $x \to \infty$. Prove that $f$ is uniformly continuous. Another way to do it: Since $f$ has a limit at $+\infty$, you can say that $f(x) = f(\tan y)$ with $y \in [0,\pi/2]$. If you denote $g: [0,\pi/2],\ g(y) = f(\tan y)$, then $g$ is continuous. Furthermore, $f(x) = g(\arctan x)$. Now use the fact that $g$ is uniformly continuous and that $|\arctan x-\arctan y| \leq |x-y|$. Apr8 comment Let $f: [0,\infty] \to \mathbb{R}$ be continuous such that its limit tends to $0$ as $x \to \infty$. Prove that $f$ is uniformly continuous. I would argue differently. For $\varepsilon>0$ choose $N$ such that $|f(x)-f(y)|<\varepsilon/2$ for $x,y >N$. Then for $[0,N]$ choose the $\delta$ corresponding to $\varepsilon/2$ from the uniform continuity property. This $\delta$, then works for all $x,y$ since if $x,y>N$ or \$x,y