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 Jan29 comment Eigenvalues of symmetric matrices are real without (!) complex numbers Not sure if it helps, but (assuming $Au = \lambda u$) by expanding $\lambda ^2 \| u \|^2$ it is not too difficult to see that $\lambda ^2 \ge 0$. At least there is no need to use conjugates if that's what you wanted to avoid. Dec3 awarded Yearling Jul2 awarded Curious Apr9 awarded Popular Question Jan30 asked Integral computation - what's going on? Dec18 accepted Determinant inequality for trace class operator Dec18 comment Determinant inequality for trace class operator That's simply terrific! Thanks a million. Answer accepted! Dec17 comment Determinant inequality for trace class operator Thank you for your reply. I don't have a positive operator, however, I have a family of operators $A(\lambda )$ where $\lambda \in \mathbb{C}$. I also happen to have $\| A (\lambda ) \|_1\le |\lambda |$ and I'm only interested in the inequality for $|\lambda |$ small. Dec17 asked Determinant inequality for trace class operator Dec12 comment Limit of an indeterminate form $\infty - \infty$. It possibly becomes more explicit if you write $x - e^x = -e^x (1-\frac{x}{e^x})$? Dec6 accepted Combinatorics and upper bound Dec6 comment Combinatorics and upper bound Just what I was looking for! Thank you so much! Dec6 revised Combinatorics and upper bound added 2 characters in body Dec6 revised Combinatorics and upper bound added 109 characters in body Dec6 asked Combinatorics and upper bound Dec3 awarded Yearling Nov6 comment Finding the complex Fourier Series Just compute $c_n=(2\pi )^{-1}\int _0 ^K 2\pi e^{-inx}\,dx$ for any $n\in \mathbb{Z}$. The answer is then $\sum _{n=-\infty }^\infty c_n e^{inx}$. Nov6 comment Showing that a map $F:C[0,1] \rightarrow \mathbb{R}^{[0,1]}$ takes $C[0,1]$ to itself. Should it be $g(x,y,f(y))$ (rather than $g(x,yf(y))$)? Nov6 comment Finding the integral of $x^2 \tan^{-1}x$ It is just a constant and hence can be included in the $C$. Nov5 accepted Can 0 be an eigenvalue?