Stephen Montgomery-Smith
Reputation
15,594
97/100 score
 Feb 26 comment Elements of SO(n) is block-diagonalizable Orthogonal matrices are normal, and hence can be diagonalized using unitary matrices. Maybe????? Feb 10 comment Proving that Pythagorean triples are relatively prime if s and t are odd I think the question might have been edited since I posted my answer. I was explaining how to show $\text{gcd}(\frac{s^2+t^2}2,\frac{s^2-t^2}2) = 1$. Jan 24 awarded Good Answer Jan 20 revised Weak $L_1$ norm is different from $L_1$ norm on a probability space j -> j/n, etc Jan 20 comment Weak $L_1$ norm is different from $L_1$ norm on a probability space I must have meant $[(j-1)/n,j/n)$. Jan 5 comment What did Whitehead and Russell's “Principia Mathematica” achieve? For an interesting (and perhaps contrarian) view, read the book by Morris Kline "Mathematics: The Loss of Certainty." Jan 2 awarded analysis Dec 30 awarded Yearling Dec 21 comment single valued analytic branch of multivalued function @User001 I am not taking the square root, I am taking a square root. Also, if $z$ is complex, then the square roots of $z^2$ are $\pm z$. The formula $\sqrt{z^2} = |z|$ is only valid if $z$ is real. Dec 13 revised Absolute convergence of fourier series Added hint Dec 13 comment Properties of Hardy operator $T(u)(x)=\frac{1}{x}\int_0^x u(t)dt$ I don't see what your problem is. Dec 13 comment Properties of Hardy operator $T(u)(x)=\frac{1}{x}\int_0^x u(t)dt$ @User1 You can choose any primitive you like, as long as you are consistent (use the same one throughout). Dec 12 comment Particular solution Look, I think you generally understand what is going on. But I have a lot going on in my life right now, so I cannot keep up this correspondence. Sorry. Dec 11 comment Particular solution If the $b_i$ are distinct, then yes, because $L\left(\sum_{i=1}^N \alpha_i e^{b_i x} \right) = \sum_{i=1}^N \gamma_i e^{b_i x}$ where the $\gamma_i$ are non-zero, and $e^{b_i x}$ are linearly independent. Dec 11 comment Particular solution Yes, that is definitely correct for constant coefficient ODE. Dec 11 comment Particular solution Yes. I think that is correct. Dec 11 answered Particular solution Dec 11 revised Absolute convergence of fourier series Define f(t) = W(t) - W(1) t. Dec 11 revised Absolute convergence of fourier series Probability 1 -> non-zero probability Dec 10 revised Absolute convergence of fourier series Made Wiener process the main theme.