Let $T\in\mathbb{R}^{n\times n}$. Show that $\rho(T) < \rho$ iff there exists a $P\succ0$ such that $ T^{\rm T}PT-\rho^2P \prec 0$.
95677
Linear Matrix Inequality of a matrix $T$ with $\| T \|_2 < \rho$
1932
How to show this equality of $\rho(X,Y)$
48593
Proof that if $s_n \leq t_n$ for $n \geq N$, then $\liminf_{n \rightarrow \infty} s_n \leq \liminf_{n \rightarrow \infty} t_n$
54791
Is it true or false that $\lvert P([0, 1]) \setminus P((0, 1)) \rvert > \lvert P(\mathbb{N}) \rvert$
20467
Show that $(y_n)\in l^q$
124844
Show that $\phi \circ f$ belongs to $L_p$ for each $f \in L_p$
153272
Basic question about $\sup_{x\neq 0}{} \frac{\|Ax\|}{\|x\|} = \sup_{\|x\| = 1}{\|Ax\|} $, $x \in\mathbb{R}^n$
10540
Prove $\vdash \neg(\square F\land p)$ in $KD$
132311
T$\mathbb{S}^{n} \times \mathbb{R}$ is diffeomorphic to $\mathbb{S}^{n}\times \mathbb{R}^{n+1}$
72551
Proof that $\rho = \pm1$ implies linear combination
38354
A result similar to Schwarz lemma
149549
Infimum of $n$-th root of $n$
118049
Show that $\mathbb{R}^{\mathbb{R}} = U_{e} \oplus U_{o}$
77891
$(U\circ T)^{*} = T^{*}\circ U^{*}$
37906
Prove $s_n$ is a Cauchy sequence for $|s_{n+1}-s_n|\lt2^{-n}$
17241
How to prove $ \prod_{d|n} d= n^{\frac{\tau (n)}{2}}$
55340
Prove that $r^n/n!$ converges where $n\ge r$