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### Questions (125)

 10 Show that the countable product of metric spaces is metrizable 10 Prove or Disprove that $\left|\frac{e^{2i\theta} -2e^{i\theta} - 1}{e^{2i\theta} + 2e^{i\theta} -1}\right| = 1$ 9 What Topology does a Straight Line in the Plane Inherit as a Subspace of $\mathbb{R_l} \times \mathbb{R}$ and of $\mathbb{R_l} \times \mathbb{R_l}$ 8 Do the singular matrices form a topological manifold 8 Understanding the Analytic Continuation of the Gamma Function

### Reputation (2,180)

 +10 Proving Holder's inequality for Schatten norms +5 Prove this matrix is invertible for $n < m-1$ +5 Extending the trace inner product to all matrix (real) inner products +5 Prove that if $X$ is subgaussian, then ${\bf E}e^{tX}=1+\sum_{k=1}^{\infty}\frac{t^k}{k!}{\bf E}X^k$

 5 Accidents of small $n$ 4 Is there a matrix $A$ such that $rank(A) < rank(A^2)$? 4 Let $M$ be a maximal ideal in $R$ such that for all $x\in M$, $x+1$ is a unit. Show that $R$ is a local ring with maximal ideal $M$ 3 What are rings good for? 2 Help me prove the identity $\overline{f(0)} = \frac{1}{2\pi}\int_0^{2\pi}\frac{e^{i\phi}}{e^{i \phi}-z}\overline{f(e^{i\phi})}d\phi$

### Tags (113)

 7 abstract-algebra × 19 3 complex-analysis × 28 5 examples-counterexamples × 3 3 ring-theory × 4 5 big-list 2 matrices × 4 4 linear-algebra × 7 1 probability × 14 4 commutative-algebra × 3 1 measure-theory × 14

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