# Tagged Questions

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102 views

### Maximize inner product of a tensor of unitary matrices

How can one maximize the following function: $f(V) = || V \otimes V - U_1 \otimes U_2 ||$ where $U_1, U_2 \in SU(n)$ are given and we seek to maximize over $V \in SU(n)$. Both the maximum value of ...
40 views

### Bounding sum of norms by the sum of sqaure of norms [closed]

How can you bound sum of norms (e.g. sum of norms of vectors) by sum of square of the same norms? Please advise. Thanks in advance.
81 views

### information measure for matrix that is analogous to rank

Is there a measure for matrix that is analogous to rank of the matrix, but it is continuous on matrix elements? Say, we could say the information in identity matrix $I_n$ is $n$, and when the off-...
45 views

### Variant of Holder's inequality [migrated]

So far I believed that only the reverse Holder inequality holds for $0<p<r<1,$ but then a student pointed out to me that $$\|x\|_p \le n^{\frac{1}{p}- \frac{1}{r}} \|x\|_r.$$ A few numerical ...
584 views

### What is the name for $(a^2 + b^2 + c^2 +…)/(a + b + c +…)$? [closed]

That is, the sum of squares of some numbers divided by the sum of the numbers. The term "anti-harmonic mean" has been coined for this quantity. I'm hoping there is a better name.
60 views

### Estimating an $L^\beta$ norm

How can we justify the following estimate \begin{align} &\left\|\int_{B(x,\epsilon)} w(y)\{(B(y)-B(x)) \cdot \nabla \rho_\varepsilon(x-y) \} \, dy \right\|_{L^\beta(B_R)} \\ &\le C \|w\|_{L^p(...
166 views

### Matrix with roots of unity entries

For given prime p, i am interested in the norms of $p \times p$ matrices which have roots of unity entries, $M_{k,l} ∈ \{1,ζ,…,ζ^{p−1}\}$ with $ζ=\exp(2πI/p)$. Are there any studies of the norms of ...
729 views

### How do you compute the dual norm of an induced norm on a subspace of a finite-dimensional $\ell^p$-normed vector space?

Say you have a finite-dimensional vector space $V$ with an $\ell^p$ norm on it. In general, the norm induced on a subspace $V_s$ of doesn't have to be another $\ell^p$ norm, so the unit sphere in $V_s$...