Erlebacher, GordonSobczyk, Garret E.2021-04-052021-04-052004-01-02Erlebacher, G., & Sobczyk, G. E. (2004). First order linear ordinary differential equations in associative algebras. <i>Electronic Journal of Differential Equations, 2004</i>(1), pp. 1-18.1072-6691https://hdl.handle.net/10877/13320In this paper, we study the linear differential equation dx/ dt = Σni=1 ai(t)xbi(t) + ƒ(t) in an associative but non-commutative algebra A, where the bi(t) form a set of commuting A-valued functions expressed in a time-independent spectral basis consisting of mutually annihilating idempotents and nilpotents. Explicit new closed solutions are derived, and examples are presented to illustrate the theory.Text18 pages1 file (.pdf)enAttribution 4.0 InternationalAssociate algebraFactor ringIdempotentDifferential equationsNilpotentSpectral basisToeplitz matrixArticle