Robert Israel
Reputation
397/400 score
 2d comment Is this a vector field? Good point: it's the vector field for a different differential equation. May 3 answered Is this a vector field? May 3 comment Is there a systematic way of finding the factorization over the closure of $\mathbb{Z}_2$ of $p(x) = x^{32} - x$? This is the kind of question that is better done by software May 3 answered An increasing smooth map $f:(0,1)\rightarrow(0,1)$ which does not extend to any smooth function on a larger domain May 3 answered Finding the number of matrices given certain conditions May 3 answered Correct notation for Continuous random variables May 3 comment What is the expectation of a product of a lognormal and a Poisson random variable If they are not independent, how are they dependent? You need to be able to specify the joint distribution. May 3 answered help with improper integral claim May 3 revised Finding a curve enclosing a given area with minimal arc length added 129 characters in body May 3 answered Finding a curve enclosing a given area with minimal arc length May 3 answered Is $\Gamma (0)^{\Gamma (0)^{-1}}$ defined at negative integers / $0$? May 2 revised How to solve the following system $\frac{\text{d}x}{\text{d} t} = -Ax + \frac{B}{y} - C$, $\frac{\text{d}y}{\text{d} t} = -Dx + \frac{E}{y} - F$ added 113 characters in body May 2 answered How to solve the following system $\frac{\text{d}x}{\text{d} t} = -Ax + \frac{B}{y} - C$, $\frac{\text{d}y}{\text{d} t} = -Dx + \frac{E}{y} - F$ May 2 comment Suppose the characteristic polynomial is $x^4$. Is it possible to get a jordan block of size$J(2)J(2)$? No, I didn't rearrange anything. What I wrote is a Jordan form with two blocks $J(2)$ and $J(2)$. The characteristic polynomial is easy to see, since the determinant of an upper triangular matrix is ... May 2 comment Which properties characterize $\sin, \cos$? You misunderstood @EricWofsey. The three conditions $f^2 + g^2 = 1$, $f(a+b) = f(a) g(b) + g(a) f(b)$, $g(a+b) = g(a) g(b) - f(a) f(b)$ are true for $\sin(cx)$ and $\cos(cx)$ as well as for $\sin(x)$ and $\cos(x)$. May 2 comment Determine the group of units of a subset of $M_n(\mathbb{C})$ @learner You mean $u \ne 0$. $1/u \in \mathbb C$ whenever $u \in \mathbb C \backslash \{0\}$. May 2 answered Given a list L of N elements uniformly sampled from a set A, what is the probability that L contains every element of A? May 2 answered The set where a derivative vanishes is G-delta May 2 comment Which properties characterize $\sin, \cos$? You'll have a hard time distinguishing $\{\cos(x),\sin(x)\}$ from $\{\cos(cx), \sin(cx)\}$ for constants $c$ without $\pi$ or some calculus: for example $\lim_{x \to 0} g(x)/x = 1$ (which is essentially the derivative at one point). May 2 comment Determine the group of units of a subset of $M_n(\mathbb{C})$ It is $\left[\matrix{a & b\cr 0 & a\cr}\right]$ where $a = 1/u$ and $b = -v/u^2$, so it fits the definition of $R$.