Eduard Weyr

Eduard Weyr

Eduard Weyr (June 22, 1852 – July 23, 1903) was a Czech mathematician now chiefly remembered as the discoverer of a certain canonical form for square matrices over algebraically closed fields.[1][2] Weyr presented this form briefly in a paper published in 1885.[3] He followed it up with a more elaborate treatment in a paper published in 1890.[4] This particular canonical form has been named as the Weyr canonical form in a paper by Shapiro published in The American Mathematical Monthly in 1999.[5] Previously, this form has been variously called as modified Jordan form, reordered Jordan form, second Jordan form, and H-form.[6]

Eduard's father was a mathematician at a secondary school in Prague, and Eduard's older brother Emil Weyr was also a mathematician. Eduard studied at Prague Polytechnic and Charles-Ferdinand University in Prague. He received his doctorate from Göttingen in 1873 with dissertation Über algebraische Raumcurven.[7] After a short spell in Paris studying under Hermite and Serret, he returned to Prague where he eventually became a professor at Charles-Ferdinand University. Eduard also published research in geometry, in particular projective and differential geometry.[1] In 1893 in Chicago, his paper Sur l'équation des lignes géodésiques was read (but not by him) at the International Mathematical Congress held in connection with the World's Columbian Exposition.[8]

Weyr canonical form

The image shows an example of a general Weyr matrix consisting of two blocks each of which is a basic Weyr matrix. The basic Weyr matrix in the top-left corner has the structure (4,2,1) and the other one has the structure (2,2,1,1).

References

  1. 1 2 Kevin C. Meara; John Clark; Charles I. Vinsonhaler (2011). Advanced Topics in Linear Algebra: Weaving Matrix Problems through the Weyr Form. Oxford University Press. pp. 94–95.
  2. ↑ O'Connor, John J.; Robertson, Edmund F., "Eduard Weyr", MacTutor History of Mathematics archive, University of St Andrews.
  3. ↑ Eduard Weyr (1885). "Répartition des matrices en espèces et formation de toutes les espèces" (PDF). Comptes Rendus, Paris. 100: 966–969. Retrieved 10 December 2013.
  4. ↑ Eduard Weyr (1890). "Zur Theorie der bilinearen Formen". Monatsh. Math. Physik. 1: 163–236.
  5. ↑ Shapiro, H. (1999). "The Weyr characteristic". The American Mathematical Monthly. 106: 919–929. doi:10.2307/2589746.
  6. ↑ Kevin C. Meara; John Clark; Charles I. Vinsonhaler (2011). Advanced Topics in Linear Algebra: Weaving Matrix Problems through the Weyr Form. Oxford University Press. pp. 44, 81–82.
  7. ↑ Eduard Weyr at the Mathematics Genealogy Project
  8. ↑ "Sur l'équation des lignes géodésiques par M. Edouard Weyr". Mathematical papers read at the International Mathematical Congress held in connection with the World's Columbian Exposition. NY: Macmillan as publisher for the AMS. 1896. pp. 408–411.
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