Fast-growing hierarchy

In mathematics, von Neumann's trace inequality, named after its originator John von Neumann, states that for any n × n complex matrices A, B with singular values ${\alpha }_1\ge {\alpha }_2\ge \cdots \ge {\alpha }_n$ and ${\beta }_1\ge {\beta }_2\ge \cdots \ge {\beta }_n$ respectively,Template:Sfn

$|\mathrm{t}\mathrm{r}\mathrm{a}\mathrm{c}\mathrm{e}(AB)|\le \sum _{i=1}^n{\alpha }_i{\beta }_i.$

(See Trace (linear algebra).)

References

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See also

• Trace inequalities

External links

• Darren Rhea, von Neumann's Trace Inequality (pdf proof)

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