Rahul
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 1d comment Is there a simpler function with this shape? What do you mean, "out of syllabus"? Apr 25 comment What are some pairs of mathematically-important functions that differ only at a few points? Then let's get this out of the way: $\lceil x\rceil$ and $\lfloor x\rfloor+1$ Apr 25 comment How to prove a regular pentagon is formed by knotting a rectangular strip of paper? Here's a purely geometrical formulation of the problem: Let the vertices of the pentagon be labeled $PQRST$ (with $P$ being the one where edges $a$ and $e$ meet). Because $QT$ and $RS$ are opposite sides of a rectangular paper strip, they are parallel and a unit distance apart. The same is true for the pairs of line segments $PQ$ and $RT$, $QS$ and $TP$, and $QR$ and $PS$. Given this information we have to prove that the pentagon $PQRST$ is regular. Apr 25 comment Maximization of quadratic form on a sphere From $x^TAx+b^Tx\le \lambda_{\max}c+b^Tx$ how do you conclude that the optimum is $x=\sqrt cv_{\max}$? Apr 21 comment Is this reflexive, symmetric, antisymmetric or transitive? What you have written is not the standard definition of an antisymmetric relation, unless you add the restriction that $z_1\ne z_2$. Apr 21 comment Proof of orthogonality in the gradient descend algorithm. It depends on how you choose $\eta$. If it is a specified constant, then the orthogonality property is not true. If instead you choose $\eta$ to minimize $E(\mathbf w_{t+1})$ at each update, then orthogonality follows from the optimality condition for $E(\mathbf w_{t+1})$. Apr 19 comment Showing that a matrix is symmetric positive definite Please stop adding and removing a tag just to bump the question to the front page. If you want to bring more attention to your question, read What should I do if no one answers my question? Apr 17 comment why is the geometric mean less than the logarithmic mean? I think you mean $\frac{b-a}{\log b-\log a}$. Apr 17 comment What is the typical $\epsilon$? Apr 16 comment Is the empty set a vector in every vector space? "According to set theory, every set must contain the empty set. So I deduce that the empty set is a member of every vector space." This is false. The empty set is a subset of every set. But it is not an element of every set. Apr 15 comment Confused about 'staircases' Apr 15 comment How does this self referencing (circular reference) equation terminate (i.e. not create a paradox?) Consider a simpler example. Suppose you have the equation $p + \frac13 N = N$. Then you can subtract $\frac13 N$ from both sides to get $p = \frac23 N$, so now you have $N = \frac32 p$. Apr 10 comment In practice, what does it mean for the Newton's method to converge quadratically (when it converges)? "when Newton's Method converges, it does so quadratically" ...as long as the derivative of the function is nonzero at the root. Apr 10 comment Set of increasing functions from N to N is uncountable $\{1,1,0,0,1,0,0,0,0,1,\ldots\}$ as a set is just $\{0,1\}$. Rather the object $[1,1,0,0,1,0,0,0,0,1,\ldots]$ you're talking about is a sequence. But then it doesn't make sense to describe it as a countable union of natural numbers. Apr 7 comment Symmetric positive semi definite implies singularity? Show that $\Sigma$ has at least one eigenvalue equal to zero. Apr 5 comment Why asymptotic notation trying to get rid off multiplicative constants? You're right though that the phrase "multiplicative constants ... are dominated" makes no sense. What is true is that in asymptotic notation, multiplicative constants are ignored. Apr 2 comment What's with this definition of ${\land}$? It's easier to see that $p\to\lnot q$ is equivalent to $\lnot(p\wedge q)$. Mar 30 comment MATLAB “back slash” computation I don't know the internals of Matlab's backslash operator, but it may have something to do with the fact that A is symmetric while A2 is not. Mar 29 comment Why is the square root of a sum not equal to the square root of each its addends? What we need here is a cure for the “law of universal linearity”. Mar 28 comment If $f$ is log-convex then $f$ is convex Apply the weighted AM-GM inequality to the right-hand side.