High Quality Content by WIKIPEDIA articles! This article collects the main theorems and definitions in linear algebra. A vector space( or linear space) V over a number field² F consists of a set on which two operations (called addition and scalar multiplication, respectively) are defined so, that for each pair of elements x, y, in V there is a unique element x + y in V, and for each element a in F and each element x in V there is a unique element ax in V, such that the following conditions hold. P.S. coefficient of the differential equation,differentiability of complex function,vector space of functionsdifferential operator, auxiliary polynomial, to the power of a complex number, exponential function.