Kravchuk Matrix
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Kravchuk Matrix

In mathematics, Krawtchouk matrices are matrices whose entries are values of Krawtchouk polynomials at nonnegative integer points.[1][2] The Krawtchouk matrix K(N) is an (N+1)×(N+1) matrix. Here are the first few examples:


In general, for positive integer , the entries are given via the generating function

where the row and column indices and run from to .

These Krawtchouk polynomials are orthogonal with respect to symmetric binomial distributions, .[3]

See also

References

  1. ^ Bose, N. (1985). Digital Filters: Theory and Applications. New York: North-Holland Elsevier. ISBN 0-444-00980-9.
  2. ^ Feinsilver, P.; Kocik, J. (2004). Krawtchouk polynomials and Krawtchouk matrices. Recent Advances in Applied Probability. Springer-Verlag. arXiv:quant-ph/0702073. Bibcode:2007quant.ph..2073F.
  3. ^ "Hahn Class: Definitions". Digital Library of Mathematical Functions.

External links



  This article uses material from the Wikipedia page available here. It is released under the Creative Commons Attribution-Share-Alike License 3.0.

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