22,711 reputation
1963
bio website math.ubc.ca/~israel
location Vancouver BC
age 64
visits member for 4 years, 5 months
seen 17 hours ago
Associate Professor Emeritus, University of British Columbia, and Optimization Algorithms Researcher, D-Wave Systems, Burnaby BC

1d
awarded  Nice Answer
1d
comment Which polynomial's roots are its coefficients?
Wrote out the equations, and solved in Maple.
1d
comment Which polynomial's roots are its coefficients?
Perhaps you mean $x^2 + x - 2$ instead of $x^2 - 2 x$, and $x^3+x^2-x-1$ instead of $x^3-x^2-x$, and excluding those where $0$ is a root.
1d
answered Which polynomial's roots are its coefficients?
2d
answered Simplifying a Taylor polynomial that involves Stirling numbers of the second kind
2d
comment Simplifying a Taylor polynomial that involves Stirling numbers of the second kind
You certainly wouldn't have just $a^n$ in the $x^n$ term. For example, for $n=2$, $$\sum_{m=1}^2 (-1)^{m-1} (m-1)! S(2,m) a^m = a - a^2$$
2d
comment Perturbed Chebyshev polynomials
Related to what @JoeSilverman wrote, $T_n(\cos \theta) = \cos(n \theta)$. You could define for non-integer $\alpha$, $T_\alpha(z) = \cos(\alpha \arccos(z))$, an analytic function on the complement of the branch cuts for $\arccos$.
Aug
31
comment Perturbed Chebyshev polynomials
$T_n$ and $f_n$ are polynomials of degree $n$. Is your $T_{\alpha_n}$ supposed to be a polynomial, and if so of what degree?
Aug
31
comment Decomposition of orthogonal matrix into 2 orthogonal matrices
For any orthogonal matrix $P$, take $Q = A^{-1} P$.
Aug
29
awarded  Nice Answer
Aug
28
answered May integration spoil real-analyticity?
Aug
19
revised when does elementwise-log preserve positive-semidefiniteness?
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Aug
18
answered when does elementwise-log preserve positive-semidefiniteness?
Aug
14
answered How many rearrangements must fail to alter the value of a sum before you conclude that none do?
Aug
12
comment Solving a nonlinear PDE numerically
Initial value ODE problems may be easier than boundary value problems. But e.g. in Maple's dsolve you don't generally need to guess an approximate solution.
Aug
11
answered How can I show that “almost all function” have property P?
Aug
11
comment Maximal Number of Pairs of Orthogonal vectors in a set of $n$ vectors in $\mathbb{R}^3$
@OlegEroshkin: You're getting $n^3/9$ pairs from $n$ vectors? I don't think so.
Aug
11
comment Maximal Number of Pairs of Orthogonal vectors in a set of $n$ vectors in $\mathbb{R}^3$
Why is that not permitted?
Aug
11
comment Version of Stone Weierstrass for functions not vanishing at infinity
Again, all continuous functions on $\mathbb R^n$ are continuous functions of bounded smooth functions, since $x_j = \tan(\arctan(x_j))$ and $\tan$ is continuous on $(-\pi/2, \pi/2)$.
Aug
11
revised Solving a nonlinear PDE numerically
added 10 characters in body