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Anton Grudkin

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22/20 answers

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187 posts edited

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366 votes cast

Answers (83)

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13	$\arctan x=\frac{1}{2}i[\ln(1-ix)-\ln(1+ix)]$
6	Derivative of product of matrix by vector
6	Sylvester's law of inertia
5	Characterization of the quasi-arithmetic mean
5	We have matrix $A\in M_{n-1\times n}(\mathbb Z)$ so that the sum of entries in each row is zero. Prove that $\det(AA^T)=nk^2.$

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Reputation (2,732)

+30	Derivative of product of matrix by vector
+25	Proving inequality: $\sum_{i=1}^n \left(a_i^7+a_i^5\right) \geq 2(\sum_{i=1}^n a_i^3)^2$
+55	$\frac{1}{(1+x)(y+z)}+ \frac{1}{(1+y)(x+z)}+ \frac{1}{(1+z)(y+x)} \geq \frac{27}{8}$
+10	Any “shortcuts” to proving that $\frac{\sin(x)}2+\sin^2(\frac x2)\tan(\frac x2)\to\tan(\frac x2)$

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Tags (93)

47 linear-algebra × 22	13 real-analysis × 5
36 matrices × 14	12 contest-math × 5
17 trigonometry × 6	11 calculus × 7
17 logarithms × 2	11 elementary-number-theory × 6
14 complex-numbers × 2	11 sequences-and-series × 5

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Bookmarks (124)

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798	How to study math to really understand it and have a healthy lifestyle with free time? [closed]
118	Real life applications of Topology
113	A multiplication algorithm found in a book by Paul Erdős: how does it work?
110	Am I just not smart enough? [closed]
83	If $a+b=1$ so $a^{4b^2}+b^{4a^2}\leq1$

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	Mathematics	2,732 rep	10 silver badges20 bronze badges
	Stack Overflow	101 rep	5 bronze badges
	TeX - LaTeX	101 rep	2 bronze badges

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Votes cast (366)

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362	up		240	question
4	down		126	answer

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