query: Prove that $\max w(2) = T_n(2),$ where $T_n$ is Chebyshev polynomial
positive_passages.docid: 155138
positive_passages.text: Chebyshev polynomials increase more quickly than any other polynomial outside $[-1,1]$
negative_passages.docid: 57096
negative_passages.text: Show that $\max{\{|a|+|b|,|c|+|d|\}} \leq \max{\{|a|,|c|\}}+\max{\{|b|,|d|\}}.$
negative_passages.docid: 153432
negative_passages.text: Question on the proof of the spectral mapping theorem for polynomials
negative_passages.docid: 118883
negative_passages.text: If $\lambda_{max} = n$, then $n\times n$ positive, reciprocal matrix A is consistent
negative_passages.docid: 36747
negative_passages.text: $\text{Tor}_0^R(M,N)\simeq M\otimes_R N$
negative_passages.docid: 118996
negative_passages.text: Prove that $T$ is an orthogonal projection
negative_passages.docid: 95266
negative_passages.text: Show $|t|\leq \pi \Rightarrow |e^{it}-1|\geq 2|t|/ \pi$
negative_passages.docid: 2455
negative_passages.text: Prove that $\left(\sum^n_{k=1}x_k\right)\left(\sum^n_{k=1}y_k\right)\geq n^2$
negative_passages.docid: 117688
negative_passages.text: Prove that $\def\Aut{\operatorname{Aut}}\Aut(\mathbf{Z_{n}})\simeq \mathbf{Z_{n}^{*}}$
negative_passages.docid: 20467
negative_passages.text: Show that $(y_n)\in l^q$
negative_passages.docid: 56211
negative_passages.text: An operator that commutes with another operator $T$ with distinct characteristic values is a polynomial in $T$
negative_passages.docid: 126197
negative_passages.text: Prove that $T$ has a cyclic vector iff its minimal and characteristic polynomials are the same
negative_passages.docid: 154487
negative_passages.text: Maximal number of monomials of multivariate polynomial
negative_passages.docid: 24128
negative_passages.text: How do i show that $w=z^2$ maps $|z-1|\leq 1$ onto $R=2(1+\cos \theta)$?
negative_passages.docid: 127397
negative_passages.text: $z\overline{w}\ne 1 $ Prove that $|\frac{w-z}{1-\overline{w}z}|\le 1|$ if $|z|\le 1$ and $|w|\le 1 $
negative_passages.docid: 103246
negative_passages.text: Prove that a polynomial of degree $d$ has at most $d$ roots (without induction)
negative_passages.docid: 113255
negative_passages.text: $X,Y\sim U(0,1)$ are independent, $W=\max (X,Y)$.