Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. This article collects the main theorems and definitions in linear algebra. A vector space( or linear space) V over a number field 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.

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