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Note on the Linear Matrix Equation

Published online by Cambridge University Press:  20 January 2009

J. H. Maclagan-Wedderburn
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The general linear matrix equation has been investigated by Sylvester in a series of interesting papers published in the Comptes Rendus. His method, however, does not show that the solution can be exhibited as an analytical function of the coefficients. The object of this note is to supply such a solution.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 22 , February 1903 , pp. 49 - 53
Copyright
Copyright © Edinburgh Mathematical Society 1903

References

* Comptes Rendus, I.C., 1884, p. 67, 115, 117, 527.Google Scholar

* Sylvester, Comptes Rendus, 1884, p. 117.Google Scholar

* Sturm, (Cours d'Analyse II., p. 146, §614)Google Scholar has obtained the same series by a somewhat similar method for the equation He, however, makes all his limits of integration the same. This series has also been obtained by different methods by other authors, e.g., Caqué, , Liouville's Journal, Ser. II., Vol. IX., 1864Google Scholar, and Fuch's, Annali di Math., Ser. II., Vol. 4, p. 46Google Scholar. See also Trans. Roy. Soc. Edin., XL., 1903Google Scholar. This method of solution can evidently be extended to equations of any order.

† Amer. Journ. of Math., Vol. XII. (1890), p. 388.Google Scholar

* Cf. Sylvester, , Amer. Journ. of Math., VI., 1884, p. 279.Google Scholar