# Tagged Questions

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### Functions that are easy to compare to a norm

Let $X$ be a subset of $\mathbb{R}^d$, let $\|\cdot \|_p$ be a norm with $1\leq p\leq\infty$, and let $f:\mathbb{R}^d\to\mathbb{R}$ be a function. I'm trying to find examples of $X$, $p$, and $f$ for ...
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### Upper semicontinuity in C(X)-algebras. Quotient norm question

upper semicontinuity in C(X)-algebras In the 5th paragraph of this post, I don't understand why there exists a vector b satisfying $||a+b||_A < ||q_x (a)||_A(x)$ By the definition of the quotient ...
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### How many values determine a norm?

It is well known that for a bilinear form over an n-dimensional vector space, $n^2$ values (on all pairs of basis-vectors) determine it uniquely. How many values do we need to specify in order to ...
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### Equivalence of entrywise 1-norm and Schatten-1 norm

Let $A \in \mathbb{R}^{m\times n}$ and $\|A\| = \sum_{i, j} |A_{i,j}|$. I am looking for constants $\alpha, \beta \in \mathbb{R}$ such that $\alpha \|A\| \leq \|A\|_* \leq \beta \|A\|$ The function ...
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In a Euclidian space (Hermitian as well), say $\ell^2_n$, the following inequality holds true $$(QI)\qquad |b|\cdot|c-a|\le|c|\cdot|a-b|+|a|\cdot|b-c|,\qquad\forall a,b,c\in\ell^2_n.$$ In other words, ...
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### On the induced matrix norm $\| \cdot \|_{2,\infty}$

The induced norm of the matrix $A$ as a map from $(\mathbb R^n , \| \cdot \|_p)$ to $(\mathbb R^m, \| \cdot \|_q)$ is given by  \| A \|_{p,q} = \sup_{x\in\mathbb{R}^n\setminus \{0\}} \frac{\|Ax\|_q}{...
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### RKHS norm and posterior of Gaussian process

In Srinivas et al (2010) [appendix B], the authors claim the following "easy to see" property relating the norm of a function in a RKHS induced by a kernel $k(\cdot,\cdot)$, and its norm in the RKHS ...