query: Show that $\|T\|=\|T^*\|$
positive_passages.docid: 155317
positive_passages.text: Norm of adjoint operator in Hilbert space
negative_passages.docid: 149801
negative_passages.text: prove that $TS = ST$
negative_passages.docid: 52791
negative_passages.text: Invertibility of an operator $T$ if $\|I-T\|<1$
negative_passages.docid: 76694
negative_passages.text: Proving that $UT=TU$ iff $U=g(T)$ for some polynomial $g$
negative_passages.docid: 45416
negative_passages.text: linear transformation $T$ is onto if and only if $T^*$ is one to one
negative_passages.docid: 51302
negative_passages.text: Show that the operator norm is submultiplicative
negative_passages.docid: 145104
negative_passages.text: $T:$ $\mathbb{C}$ $\to$ $\mathbb{C}$ by $T(z)=\lambda z + \mu \bar{z}$ for every $z \in \mathbb{C}$
negative_passages.docid: 2315
negative_passages.text: How to prove that $\lVert x + y\rVert = \lVert x\rVert + \lVert y \rVert \implies \lVert tx + (1-t)y\rVert = t\lVert x\rVert + (1-t)\lVert y \rVert$?
negative_passages.docid: 76188
negative_passages.text: Show $(W_1 + W_2 )^\perp = W_1^\perp \cap W_2^\perp$ and $W_1^\perp + W_2^\perp ⊆ (W_1 \cap W_2 )^\perp$
negative_passages.docid: 46265
negative_passages.text: Minimal polynomial of the operator $T:V\oplus W\to V\oplus W$
negative_passages.docid: 95677
negative_passages.text: Linear Matrix Inequality of a matrix $T$ with $\| T \|_2 < \rho$
negative_passages.docid: 97158
negative_passages.text: Prove that the operator norm is a norm
negative_passages.docid: 3820
negative_passages.text: Prove that $||x|-|y||\le |x-y|$
negative_passages.docid: 73406
negative_passages.text: Prove that $E_{\lambda}(T)=E_{\lambda^{-1}}(T^{-1})$ if $T$ is an invertible linear operator on a finite dimensional vector space $V$
negative_passages.docid: 120010
negative_passages.text: Show that $\aleph_{\alpha}^{\aleph_{1}} = \aleph_{\alpha}^{\aleph_{0}}\cdot 2^{\aleph_1}$
negative_passages.docid: 130045
negative_passages.text: Show that $l^2$ is a Hilbert space
negative_passages.docid: 37813
negative_passages.text: If $T\colon \mathbb R^n \to \mathbb R^n $ linear and $T^2 = kT$