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". http://mathworld.wolfram.com/SpijkersLemma.html. 

References

• Wegert, Elias; Trefethen, Lloyd N. (February 1994). "From the Buffon Needle Problem to the Kreiss Matrix Theorem". The American Mathematical Monthly 101 (2): 132–139. doi:10.2307/2324361. https://ecommons.cornell.edu/bitstream/1813/7113/1/92-1273.pdf.