Topic
Krawtchouk matrices
About: Krawtchouk matrices is a research topic. Over the lifetime, 11 publications have been published within this topic receiving 99 citations.
Papers
TL;DR: Symmetric Krawtchouk matrices as discussed by the authors were introduced as a modification of the Krawchouk polynomials, whose entries are values of the krawchkouk coefficients.
24 citations
TL;DR: The Walsh decomposition of pseudo-Boolean functions and properties of Krawtchouk matrices are used to exactly compute the expected value for the fitness of a child generated by uniform crossover followed by bit-flip mutation from two parent solutions.
16 citations
TL;DR: In this article, the existence of two natural bilinear forms on the space of spinors has been shown for a real representation of the Clifford algebra corresponding to p+q with metric of signature (p, q).
Abstract: Given a real representation of the Clifford algebra corresponding to \({\mathbb{R}^{p+q}}\) with metric of signature (p, q), we demonstrate the existence of two natural bilinear forms on the space of spinors. With the Clifford action of k-forms on spinors, the bilinear forms allow us to relate two spinors with elements of the exterior algebra. From manipulations of a rank four spinorial tensor introduced in [1], we are able to find a general class of identities which, upon specializing from four spinors to two spinors and one spinor in signatures (1,3) and (10,1), yield some well-known Fierz identities. We will see, surprisingly, that the identities we construct are partly encoded in certain involutory real matrices that resemble the Krawtchouk matrices [2][3].
3 citations
Posted Content•
TL;DR: In this paper, an algebraic characterization of Krawtchouk matrices in terms of split quaternions is given, and the resulting properties include an easy inference of the spectral decomposition.
Abstract: An interpretation of Krawtchouk matrices in terms of discrete version of the Feynman path integral is given. Also, an algebraic characterization in terms of the algebra of split quaternions is provided. The resulting properties include an easy inference of the spectral decomposition. It is also an occasion for an expository clarification of the role of Krawtchouk matrices in different areas, including quantum information.
3 citations
TL;DR: In this article, a class S N of matrices whose elements are terms of convolutions of binomial functions of complex numbers is introduced, and a multiplication theorem is proved for elements of S N.
3 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2016 | 1 |
| 2014 | 1 |
| 2012 | 4 |
| 2008 | 1 |
| 2007 | 1 |
| 2005 | 1 |