ALGEBRE 2 (F)
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Geometry predominated in Greek mathematics and it was not until Descartes
in the 17th century to make the link, thanks to the notion of reference, between geometric notions:
points of the plane or space, curves and algebraic ones, couples or triplets of real numbers
and equations. This approach proved fruitful for both surveyors and analysts.
It offered the first all the power of analysis to deal with geometry problems.
and, in the second, the representations of geometry to visualize and state the phenomena of
the analysis. The generalization of the geometric notions of the plane R3 and the space R3 to spaces
of larger size was not immediate. The formalism was lacking to be able to address
this problem. It was the self-taught German mathematician Hermann Grassmann who, at
19th century, outlined the notions of vector space and dimension. His work was firstly
difficult and it is thanks to the Italian mathematician Giuseppe Peano that these concepts became clearer
and took their final form. Linear algebra has become the framework of study for many
theories, particularly in analysis. Today, with the development of computer tools,
Linear algebra is implemented more easily thanks to matrix calculation.
This chapter covers some of the fundamentals required for this document. Mastery
of the material in this chapter is essential. The concepts covered are:
— Vector spaces.
— Vector subspaces.
— Base and Dimension of a vector space.
— Sum of vector subspaces. -
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