126,865 reputation
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bio website math.ubc.ca/~israel
location Richmond, Canada
age
visits member for 3 years, 5 months
seen 5 hours ago

I'm an Emeritus Associate Professor of Mathematics at University of British Columbia and an Optimization Algorithms Researcher at D-Wave Systems in Burnaby BC


5h
revised A subring of the ring of Gaussian integers such that $a^2 \mid b^2$ does not lead to $a\mid b$ in infinitely many such cases
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5h
answered A subring of the ring of Gaussian integers such that $a^2 \mid b^2$ does not lead to $a\mid b$ in infinitely many such cases
6h
answered Does $\sum_{i=1}^\infty a_i/i < \infty$ imply that $a_i$ has Cesaro mean zero?
9h
answered Smallest value taken by a quadratic polynomial in two variables.
11h
answered Banach Spaces: Totally Bounded Subsets
11h
comment What happens to a function when it is undefined?
@Jona: $\sqrt{2}$ is not "infinite". It is a perfectly good real number. The fact that it can't be exactly represented in your calculator is irrelevant to questions of definition. On the other hand, it is true that in numerical calculations you have to be very careful with expressions in which you take the difference of two numbers that are very close to each other, causing a large relative error. That is an entirely separate question.
11h
revised Solve for $\theta$: $a = b\tan\theta - \frac{c}{\cos\theta}$
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11h
answered Solve for $\theta$: $a = b\tan\theta - \frac{c}{\cos\theta}$
12h
comment finite sum of cosines
Watch out for the case where $k$ divides $n$.
12h
answered finite sum of cosines
14h
comment polynomials and minimality
You could say that $1 + x + x^4$ is the minimal polynomial of a certain root $r$ of $x^{15}-1$ in some extension field of ${\mathbb Z}_2$. Such an $r$ would satisfy $1 + r + r^4 = 0$. It would not satisfy $1 + r^3 + r^4 = 0$, so $1+x^3+x^4$ would not be a minimal polynomial of $r$.
14h
comment polynomials and minimality
Your edit didn't change the main point: $1 + x + x^4$ is not "a minimal polynomial of $x^{15} - 1$" in ${\mathbb Z}_2[x]$. It is a prime factor of $x^{15} - 1$, but so are $1 + x$ and $1 + x^3 + x^4$ and $1 + x + x^2$.
14h
answered Do mathematics researchers regularly solve problems like this?
14h
comment Is there a theorem about eigenvalues of sum of matrices?
No. In my construction, the eigenvector of $A+B$ for $\lambda_i$ is an eigenvector of $A$, but for a different eigenvalue. For example, for $A = \pmatrix{1 & 0 & 0\cr 0 & 2 & 0\cr 0 & 0 & 3\cr}$ you could take $B = \pmatrix{1 & 0 & 0\cr 0 & 1 & 0\cr 0 & 0 & -2\cr}$.
17h
revised Is there a theorem about eigenvalues of sum of matrices?
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18h
answered Is there a theorem about eigenvalues of sum of matrices?
18h
comment Solving a system of polynomial equations in three variables (x^2-yz=18, y^2-zx=8, z^2-xy=-7)
Perhaps you think "your work" should consist of asking the question here?
18h
comment Convergence sequence of random variables
For $n > m$, $X_n = a^{n-m} X_m + $(something independent of $X_m$), so $\text{Cov}(X_n, X_m) = a^{n-m} \text{Var}(X_m)$.
1d
answered What is the greatest common divisor of $3^{3^{333}}+1$ and $3^{3^{334}}+1$?
1d
answered How to find a closed form of this simple factorial sequence