Following the wiki-link treasure hunt leads me to topics such as "p-norms on finite dimensional vector spaces".
Which makes me want to ask: what's a good textbook or reference where I can learn more about the p-norms on finite dimension vector spaces? I need to learn enough in order to answer the following questions given a proposed induced norm:
0) Why is it that in general $\|Ax\| \leq \|A\|\|x\|$ (where $\|A\|$ is the matrix norm, and $\|x\|$ is the vector norm)?
1) is the proposed induced norm a norm? (I think I know how to check for this now, as the Wikipedia page tells me what requirements a norm must satisfy to be considered one.)
2) given a proposed induced norm on a matrix, what is the corresponding vector norm?
Could you recommend a good resource to learn (notes, or textbook, or whatever)?
A textbook that is self-contained would be particularly valuable, but if I had to choose between an insightful text that was not self-contained, and a needlessly opaque text that was self-contained, I would pick the latter.