Local Inversion Theorem

This lecture covers the Local Inversion Theorem, which states that if the determinant of the derivative of a function is non-zero at a point, then the function is a local diffeomorphism at that point. The theorem is illustrated through examples and proofs, emphasizing the concept of local invertibility and the conditions for a function to be a diffeomorphism. The lecture also discusses the equality of two non-singular matrices and the uniqueness of solutions in differentiable functions. Additional topics include the properties of matrix norms and the concept of unique solutions in differential equations.