Jan 24, 2013 · We can define the norm of a complex number in other ways, provided they satisfy the following properties. Positive homogeneity. Triangle inequality. Zero norm iff zero vector. …

So every vector norm has an associated operator norm, for which sometimes simplified expressions as exist. The Frobenius norm (i.e. the sum of singular values) is a matrix norm (it …

The norm you describe in your post, $||\epsilon||=\max|\epsilon_i|$ is a particular norm that can be placed on $\mathbb{R}^n$; there are many norms that can be defined on $\mathbb{R}^n$. …

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I know the definitions of the $1$ and $2$ norm, and, numerically the inequality seems obvious, although I don't know where to start rigorously. Thank you. analysis

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There are infinitely many norms that satisfy your requirements, and some of them are not invariant under right-multiplication of orthogonal matrix.

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Jul 7, 2014 · Hence $\cup_{ p \ge 1 } B_p(0,1)$ is bounded, balanced, convex and contains $0$ in its interior, and so is the unit ball of some norm, in this case, $\|\cdot \|_\infty$. The point here …

Dec 17, 2017 · I've read the Uniform Norm Wikipedia page, but my most of it went over my head. What is the sup-norm in simple and / or intuitive terms? Are there any good examples which …