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amsmath
  • Member for 6 years, 8 months
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12 votes
Accepted

Calculating the integral with an undefined function f(x)

9 votes

How to find the limit of series? (What should I know?)

9 votes
Accepted

How do I prove that $|\det(A+B)|\leq2^n$ where $A,B$ are $n\times n$ unitary matrices?

8 votes

Show that $A^{-1} + B^{-1}$ is invertible when $A,B$ and $A+B$ are invertible

8 votes
Accepted

Calculate $\lim_{x\to 0} {1\over x} \int_0^x \cos(t^2)\,dt$

7 votes

The convolution of two $L^2(\mathbb R)$ functions is continuous

7 votes
Accepted

$X$ is a random variable, if $\Bbb E(X^2)=1$ and $\Bbb E(X)\geq a>0$, prove that $\Bbb P(X\geq\lambda a)\geq(a-\lambda a)^2$ for $0\leq\lambda\leq 1$.

6 votes
Accepted

Inverse of an "anti-Jordan" matrix

5 votes
Accepted

Showing that given matrix does not have negative eigenvalues without using the knowledge that it is positive definite.

5 votes
Accepted

Let $F$ be a field with four elements $F = \{0,1,a,b\}$. What is $a^2 + a$?

5 votes
Accepted

How to see that group of unitary operators with strong operator topology is connected?

5 votes

Showing $\lim_{n\to \infty} \left( 1+\frac{1}{2n} \right)^n = \sqrt{e}$, intro to analysis

5 votes
Accepted

The average of a function over a sphere tends to its value at the center, as the radius goes to zero

5 votes
Accepted

Can we reconstruct a function $f$ by knowing its scalar product with its own shift, $\langle T_xf,f \rangle$?

5 votes
Accepted

Prove that $\| v \|_{1} \|v\|_\infty \leq \frac{1+\sqrt{n}}{2} \|v\|^{2}_{2}$

5 votes
Accepted

An example of a trigonometric series that is not a Fourier series

4 votes
Accepted

Norm of linear map $f:R^n \rightarrow R^m$ from its matrix

4 votes
Accepted

Solve functional equation $f(x)+f(y)=f(x\sqrt{1-y^2}+y\sqrt{1-x^2})$

4 votes
Accepted

Rearrangement of divergent series with positive terms.

4 votes

A fascinating sequence of polynomials

4 votes
Accepted

Proof of $\|P\| \leq \|I-P\|$ for L2 norm in Hilbert space when $P$ is a projection

4 votes
Accepted

Controllability set of a restricted control problem

4 votes
Accepted

A version of Poincaré's inequality in one dimension

4 votes
Accepted

Weak Operator Convergence Example

4 votes
Accepted

Is the integration of Lipschitz function still Lipschitz?

4 votes
Accepted

Prove that the eigenvalues of a product of positive semidefinite matrices are nonnegative

4 votes

Eigenvalue of normal matrices

4 votes
Accepted

Bound on eigenvalues of $A+A^*$ for $A$ unitary

4 votes
Accepted

Show that $f(x)=x^r+r^x$ is increasing

3 votes
Accepted

Prove that the following R linear map is an isometry.

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