# Tagged Questions

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### Relation between the subordinate norm and the spectral radius of a matrix

Let's define the following subordinate norm of a $(NM \times NM)$ matrix A norm as follows \begin{eqnarray*} ||A||_{2,b} = \mathrm{max}_{x \in \mathbb{C}^{NM}} \left \{ \frac{||A x||_b}{||x||_2} ...
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### Relation between the block maximum norm and the Euclidean norm of a matrix

I am trying to give answer to the following question: Let's define de block maximum norm of a $N*M \times N*M$ matrix as \begin{eqnarray*} \parallel A \parallel_b = max_{x \neq 0} [ \parallel A x ...
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### Approximation with a rank-$1$ matrix

Given a matrix $A$ (generally speaking, complex and non-square), I want to find an identically-sized matrix $D$ with ${\rm rk} D\le 1$ to minimize the induced operator norm $\|A-D\|_2$. From the ...
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Let $T$ be a linear operator acting on a finite-dimensional real or complex vector space. As a direct consequence (or rather a particular case) of the Riesz-Thorin theorem, we have $$\|T\|_2 \le ... 1answer 317 views ### Hölder's inequality for matrices I was wondering if the HÃ¶lder's inequality was true for matrix induced norms, i.e. if$$\|AB\|_1 \leq \|A\|_p\|B\|_q, \quad\forall p,q \in [1,\infty] \text{ s.t. } \tfrac{1}{p}+\tfrac{1}{q} = 1.$$But ... 2answers 148 views ### Matrix-Norm aquivalence with p-Norm [closed] Let A be a square Matrix and ||\cdot ||_p the induced Matrixnorm for 1 \leq p \leq \infty. Is it true that$$||A||_p\leq \max(||A||_1,||A||_{\infty})? For $p=2$ the answer is yes because ...
Problem Formulation under what conditions can we solve $\mathrm{trace}(\mathbf{AB})=0$ ? or more specifically, when will $\mathrm{trace}(\mathbf{AB})=0$ implies that $\mathrm{trace}(\mathbf{B})=0$. ...
Suppose I have an $d$-regular expander graph with $n$ vertices, where the stochastic version of its adjacency matrix $A$ (with entries $1/d$ and zero) has second eigenvalue $\lambda$. Let \$x \in ...