Spijker's lemma

In mathematics, Spijker's lemma is a result in the theory of rational mappings of the Riemann sphere. It states that the image of a circle under a complex rational map with numerator and denominator having degree at most n has length at most 2nπ.

Applications

Spijker's lemma can be used to derive a sharp bound version of Kreiss matrix theorem.

See also

• Buffon's needle

External links

• Weisstein, Eric W. "Spijker's Lemma". MathWorld.

References

• Wegert, Elias; Trefethen, Lloyd N. (February 1994). "From the Buffon Needle Problem to the Kreiss Matrix Theorem" (PDF). The American Mathematical Monthly. 101 (2): 132–139. doi:10.2307/2324361. hdl:1813/7113. JSTOR 2324361.