%0 Journal Article
%T First order linear ordinary differential equations in associative algebras
%A Gordon Erlebacher
%A Garrret E. Sobczyk
%J Electronic Journal of Differential Equations
%D 2004
%I Texas State University
%X In this paper, we study the linear differential equation $$ frac{dx}{dt}=sum_{i=1}^n a_i(t) x b_i(t) + f(t) $$ in an associative but non-commutative algebra $mathcal{A}$, where the $b_i(t)$ form a set of commuting $mathcal{A}$-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.
%K Associative algebra
%K factor ring
%K idempotent
%K differential equation
%K nilpotent
%K spectral basis
%K Toeplitz matrix.
%U http://ejde.math.txstate.edu/Volumes/2004/01/abstr.html