query: About the spectrum $\sigma(T)$
positive_passages.docid: 19294
positive_passages.text: ‎If ‎‎$‎X$ is an infinite-dimensional Banach space and ‎‎$‎‎u‎\in ‎B(X)‎$ ,then $\bigcap_{v\in K(X)}\sigma(u+v) =\cdots$
negative_passages.docid: 157599
negative_passages.text: what is the meaning of $F_\sigma$ and $G_\delta?$
negative_passages.docid: 56943
negative_passages.text: Normal operator with real spectrum is hermitian.
negative_passages.docid: 36131
negative_passages.text: $\sigma$-algebra vs. $\sigma$-field: is there any difference?
negative_passages.docid: 115860
negative_passages.text: Is a measure for a sigma algebra determined by its values for a generator of the sigma algebra?
negative_passages.docid: 144097
negative_passages.text: eigenvalues and eigenvectors of $vv^T$
negative_passages.docid: 95266
negative_passages.text: Show $|t|\leq \pi \Rightarrow |e^{it}-1|\geq 2|t|/ \pi$
negative_passages.docid: 108921
negative_passages.text: By substituting $z = h(t)$ show that $\delta(h(t))=\sum\limits_{i}\frac{\delta(t−t_i)}{\mid h^{\prime}(t_i)\mid}$
negative_passages.docid: 18939
negative_passages.text: Eigenvalues of the transpose
negative_passages.docid: 38850
negative_passages.text: How to show Von Neumann Trace inequality $ \text{Tr}(AB) \leq \sum_{i=1}^n \sigma_{A,i}\sigma_{B,i} $?
negative_passages.docid: 30996
negative_passages.text: If $\langle Ta, a\rangle \in \mathbb{R}$ for all $a$ then $T$ is self-adjoint
negative_passages.docid: 45998
negative_passages.text: The range of $T^*$ is the orthogonal complement of $\ker(T)$
negative_passages.docid: 124164
negative_passages.text: ($n$-dimensional) Inverse Fourier transform of $\frac{1}{\| \mathbf{\omega} \|^{2\alpha}}$
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: 35140
negative_passages.text: Existence of minimal $\sigma$-algebra and transfinite induction
negative_passages.docid: 55377
negative_passages.text: Non-zero eigenvalues of $AA^T$ and $A^TA$
negative_passages.docid: 51134
negative_passages.text: If $E \in \sigma(\mathcal{C})$ then there exists a countable subset $\mathcal{C}_0 \subseteq \mathcal{C}$ with $E \in \sigma(\mathcal{C}_0)$