Editing Matrix norm (section)

===Examples of norm equivalence===
Let <math>\|A\|_p</math> once again refer to the norm induced by the vector ''p''-norm (as above in the Induced norm section).

For matrix <math>A\in\R^{m\times n}</math> of [[Rank (linear algebra)|rank]] <math>r</math>, the following inequalities hold:<ref>
[[Gene Golub|Golub, Gene]]; [[Charles Van Loan|Charles F. Van Loan]] (1996). Matrix Computations – Third Edition. Baltimore: The Johns Hopkins University Press, 56–57. {{ISBN|0-8018-5413-X}}.</ref><ref>Roger Horn and Charles Johnson. ''Matrix Analysis,'' Chapter 5, Cambridge University Press, 1985. {{ISBN|0-521-38632-2}}.</ref>

*<math>\|A\|_2\le\|A\|_F\le\sqrt{r}\|A\|_2</math>
*<math>\|A\|_F \le \|A\|_{*} \le \sqrt{r} \|A\|_F</math>
*<math>\|A\|_{\max} \le \|A\|_2 \le \sqrt{mn}\|A\|_{\max}</math>
*<math>\frac{1}{\sqrt{n}}\|A\|_\infty\le\|A\|_2\le\sqrt{m}\|A\|_\infty</math>
*<math>\frac{1}{\sqrt{m}}\|A\|_1\le\|A\|_2\le\sqrt{n}\|A\|_1.</math>