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This lecture covers the concept of invertible linear applications between finite-dimensional vector spaces, highlighting that the dimensions of the spaces must be equal for an application to be bijective. The lecture also discusses the conditions for a linear application to be bijective, focusing on the invertibility of the corresponding matrix. Through examples, the instructor demonstrates the properties of orthogonal symmetry transformations and their inverses, emphasizing the relationship between the matrices representing these transformations. The lecture concludes by showcasing how certain linear applications are their own inverses.