Grupos matriciais são variedades diferenciáveis. - ALMEIDA, Ândson José Silva (2024)
The principal objective of this project is to demonstrate that matrix groups have the structure of differentiable manifolds. Our focus is to develop the mathematical tools necessary for the understanding of the statement of this theorem and its demonstration, for instance: the differentiation in finite dimensional real vector spaces, sequences and series of vectors and some algebraic results. Also, we put emphasis to prove the important results that are fundamental in the development of the theory of matrix groups, such as the Inverse Function Theorem and the smoothness of the matrix exponential.