Yaroslav Bulatov's user avatar
Yaroslav Bulatov's user avatar
Yaroslav Bulatov's user avatar
Yaroslav Bulatov
  • Member for 13 years, 6 months
  • Last seen this week
70 votes
5 answers
47k views

Matrices commute if and only if they share a common basis of eigenvectors?

13 votes
1 answer
945 views

Proving $\sqrt{1-x^2}\ge \operatorname{erf}(\sqrt{-\log x})$

13 votes
2 answers
304 views

Inverse of integral transform $f(s)=\int_0^\infty g(x) \exp(-s g(x)) \mathbb{d}x$

12 votes
3 answers
573 views

Average value of $\frac{x'A^2x}{x'A^3x}$ over surface of $n$-dimensional sphere

12 votes
2 answers
277 views

Why is $AA^TAA^TAA^TAA^T$ larger than $AAAAA^TA^TA^TA^T$ for Gaussian $A$?

11 votes
3 answers
629 views

Computing $\int _0^{\infty }e^{-b x} x^{b-1} \log \left((1-a x)^2\right)dx$ or $ \mathbb E \log\left[(c- \chi^2_{2b} )^2\right]$

9 votes
3 answers
501 views

Behavior of inverse of $f(s)=\frac{1}{H_n}\sum_{i=1}^n \left(1-\frac{1}{i}\right)^s\frac{1}{i}$

9 votes
1 answer
200 views

What is $E[1/\|x\|^4]$ where $x\sim$ Gaussian($0,C\cdot $diag($1,1/2,1/3,1/4,\ldots$))?

9 votes
3 answers
2k views

Proving $1-\exp(-4x^2/ \pi) \ge \text{erf}(x)^2$

9 votes
3 answers
2k views

Implementing trig functions for dual numbers

8 votes
1 answer
3k views

Second order approximation of $\log \det X$

8 votes
3 answers
905 views

Limit of Gamma integrals

8 votes
2 answers
277 views

Showing $E\operatorname{Tr}(AAA^TA^T)=n^3 + 2n$

7 votes
2 answers
287 views

Frobenius norm of a product of Gaussian matrices

7 votes
1 answer
465 views

Solving $\frac{\partial}{\partial t} f =hf+ h \int \mathrm {d} i\, h f$

6 votes
0 answers
158 views

Geometric interpretation of a non-symmetric matrix having only real eigenvalues?

6 votes
1 answer
172 views

Convergence from spectrum of the Choi matrix?

6 votes
1 answer
292 views

When does $\prod_i (1-\alpha X_i^2)^2\overset{P}{\rightarrow} 0$ for some $\alpha$?

6 votes
1 answer
5k views

Meaning of Lagrange multiplier always being 0?

6 votes
3 answers
2k views

discrete version of Laplacian

6 votes
1 answer
865 views

Getting generators of graphs automorphism group

6 votes
1 answer
242 views

Showing that $\cos(u_1,u_3)=\cos(u_1,u_2)\cos(u_2,u_3)$ for nearby $u_i$

6 votes
0 answers
334 views

Estimate nearly-singular Gaussian covariance matrix

5 votes
4 answers
174 views

Behavior of $\sum_i^n (1-\frac{1}{i})^s$ as a function of $s$?

5 votes
2 answers
125 views

Is this function bounded? $g(n)=t>1\text{ s.t. } \int_1^n (1-i^{-p})^t i^{-p} \, di =\varepsilon$

5 votes
1 answer
171 views

Conditions for $I-x A$ to be a convergent matrix for some $x\in \mathbb{R}$

5 votes
0 answers
101 views

Sampling from intersection of sphere and simplex

5 votes
1 answer
110 views

Minimizing $\frac{\operatorname{Tr}(H^2)^2}{\operatorname{Tr}(H^3)\operatorname{Tr}H}$

5 votes
2 answers
152 views

Minimizing $\frac{\|p\|_2^2}{\|p\|_\infty}$ for probability vector $p$

5 votes
3 answers
2k views

Diagonal of an inverse of a sparse matrix

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