# Tagged Questions

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### Prove relative error with condition number of matrix inequality

I was working on some questions and solutions, and encountered the following question. I am able to prove the inequality using the given information and some algebraic manipulation but the "within ...
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### Pareto distribution and matrix

I am wondering if there are any bounds are known on the eigenvalues of random matrix whose entries are with Pareto distribution? Thank you.
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### Inequality matrix norm

Let $A$ be an $n\times n$ random matrix $A=rand(n,n)$. Let $\alpha=max_{i,j}|a_{ij}|$ (i.e, $\alpha$ is the largest entry in $A$ in absolute value).I need to show that $\ \alpha < \| A \|_{2}$. ...
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### Matrix norm of product equal implies equality in norms of factors

Given a matrix $A$, if $$\|Av\|_1=\|Aw\|_1$$ for given vectors $v$ and $w$, then does $\|v\|_1=\|w\|_1$? Here $\|\,\cdot\,\|_1$ denotes the $L^1$ norm.
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### Plot of ||X||infinity norm

Can anybody tell me why the plot of $\|X\|_{\infty}$ in $\mathbb{R}^2$ comes out to be square? Since $\|(x_1,x_2)\|_{\infty} = \max\{|x_1|,|x_2|\}$, then let us say $|x_1|$ is max. Why the plot is ...
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### Condition Number of a block Matrix

Is this hypothesis true? $$cond([A,B])≤cond(A)+cond(B)$$ where $cond$ is the Condition Number. And is this true for rectangular matrices($nxm$)? Let's consider $3$ different conditions for $A$ and ...
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### Asymptotic behavior of $L^2$ norm for increased matrix dimensions
I am playing with matrices which are linear combinations of identity matrix, Pauli spin matrices, $\sigma_x$ and $\sigma_z$ or their tensor products. For example, let the matrix be $H$. So, $H$ could ...
Let $\{u_i\}_{i=1}^n$ be a set of orthonormal basis and $M$ a symmetric matrix. Suppose $$\left|\langle u_iu_i^T,M\rangle\right|\leq \tau\ \ \forall i=1,\dots,n.$$ Can I ...