Editing Algebra representation (section)

=== Linear complex structure ===
{{main|Linear complex structure}}
One of the simplest non-trivial examples is a [[linear complex structure]], which is a representation of the [[complex number]]s '''C''', thought of as an associative algebra over the [[real number]]s '''R'''. This algebra is realized concretely as <math>\mathbb{C} = \mathbb{R}[x]/(x^2+1),</math> which corresponds to {{math|1={{mvar|i}}<sup>2</sup> = −1}}. Then a representation of '''C''' is a real [[vector space]] ''V'', together with an action of '''C''' on ''V'' (a map <math>\mathbb{C} \to \mathrm{End}(V)</math>). Concretely, this is just an action of {{mvar|i}} , as this generates the algebra, and the operator representing {{mvar|i}} (the [[Image_(mathematics)#Image_of_an_element|image]] of {{mvar|i}} in End(''V'')) is denoted ''J'' to avoid confusion with the [[identity matrix]] ''I''.