Lecture
This lecture covers elementary linear algebra concepts related to matrices, including invertible connections, elementary matrices, matrix rank, transposition, and the invariance of rank by transposition. It explains the properties of transposition, anti-multiplicativity, and the relationship between matrix rank and the dimension of the space generated by the matrix. The lecture also discusses the transformation of columns into rows through transposition and the corollary stating that the rank of a matrix equals the dimension of the space it generates. Additionally, it explores examples of rank matrices and the dual map matrix in different bases.