Um estudo sobre o produto geométrico e algumas aplicações

Abstract

The main purpose of this work is to present, in a simple way, the relationship between geometric algebra and analytical geometry and linear algebra. In a special way, our purpose was to highlight where and how the action of geometric algebra allows us to draw conclusions, descriptions and make interpretations about geometrics facts. In order to do this, we have based our studies on the assumptions of Clifford’s Algebra (1845-1879). First of all, we remember the essential concepts of linear algebra. Afterward, we brought to light the conception of Clifford’s algebras, listing some properties and showing how the geometric product work. Finally, we present some applications for bidimensional and tridimensional geometry. So, we realized the power of Clifford’s algebras in problems related to geometry and physic due to the hardness of its algebraic tools and also, by the elegance that it describes the main concepts of Descartes analytical geometry.