I'm reading a problem which uses the matrix norm induced by the maximum norm for $\mathbb{R}^n$. But I do know what it is exactly, and googling it gives different results.
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$\begingroup$The matrix norm described in your textbook is what is described at the beginning of the Wikipedia article. (Note that any norm on the vectors will induce a norm on the matrices.)
The "entrywise norms" that the article describes later are not norms in this sense. They aren't induced by vector norms. As the article points out sometimes the same notation is used for different things. The "max norm" is one of these entrywise norms.
The max norm just treats the matrix as if it were a vector, with the entries written in a rectangular array instead of a line. It doesn't have anything to do with the matrix as an operator on vectors.
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