# Questions tagged [operator-norms]

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### Does this matrix norm inequality have interesting application in other areas of mathematics?

In my new paper, one of the main theorems gives an upper bound for the spectral distance of a general real symmetric matrix to diagonal matrices: Theorem 3. ‎Let $A=[a_{ij}]$ be a real symmetric ...
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### Schatten norm inequality

Let $A,B$ be two $n\times n$ matrices. Find a lower bound of the $p$-th Schatten norm $\|(A-B)(A-B)^\ast\|_{S_{p/2}}^{1/2}$ in terms of Schatten norm of $\|(AA^*+BB^*)\|_{S_q}$ for any relation ...
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### How to numerically compute the operator norm of an operator acting on a matrix algebra?

Let $M_n(C)$ denote the $n\times n$ matrices with complex entries acting on the Hilbert space $C^n$. As norm on $M_n(C)$ we take the operator norm, i.e. the largest eigenvalue of its absolute value. ...
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### Explicit description for dual to operator space of Hilbert space

Let $H$ be a separable Hilbert space, and $B := \mathcal B(H)$ be the space of bounded operators on $H$. It is known that $B^\ast_\mathrm{strong} = B^\ast_\mathrm{weak}$ (see [Dunford, Schwartz, VI.1....
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### Tail bound on trace norm / nuclear norm / Schatten-1 norm of Rademacher matrix

Let $0 < r \leq d$ integers. Let $X$, $Y$ be $d \times r$ matrices of independent Rademacher variables, that is, $X,Y \in \mathbb{R}^{d \times r}$ with entries $\pm1$ with probability $1/2$. I am ...
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### Application of the Frechet derivative [closed]

$f\colon U\subset \mathbb{R}^{n}\longrightarrow\mathbb{R}^{m}$ is differentiable at $x_{0}$ if there exist a linear transformation $T\colon \mathbb{R}^{n}\longrightarrow\mathbb{R}^{m}$, such that: \...
1 vote
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### Equivalence constants for induced matrix norms

Disclaimer: I asked this question beforehand on mathematics stack exchange, but I think it is better suited for this site Given two sets $P_i\in\mathbb{R}^s$, bounded, convex, with non-empty interior ...
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### Operator norm of a masked SDP matrix

Let $\Sigma$ be a $d\times d$ semi-definite positive matrix (SDP). Let $I\subset\{1,\ldots, d\}\times \{1, \ldots, d\}$ be a symmetric subset of indices (i.e. if $(p,q)\in I$ then $(q,p)\in I$). We ...
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### Hierarchies of Operator Norms [closed]

Given some linear operator $T: V \mapsto W$, we can talk about the operator norm between the spaces V and W, i.e.  \| T \|_{V \mapsto W} \ = \ \sup_{g} \| Tg \|_W \ , \quad \mbox{ with } \| g \|_V \...
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### Operator norm for $\max\frac{\Vert x \Vert _1}{\sqrt {x'Cx}}$
Suppose $C$ is a $n$ by $n$ real symmetric matrix, and $x\in R^n$. Is there an operator norm of $C$ for $\max\frac{\Vert x \Vert _1}{\sqrt {x'Cx}}$? If I decompose $C$ into $A'A = C^{-1}$, It seems ...