Determinants: Properties and Operations

This lecture covers the definition of determinants for square matrices, including the scalar determinant, the determinant relative to column vectors, and the determinant relative to row vectors. It also explores properties such as homogeneity, invariance by transposition, multiplicativity, and the criterion for invertibility. The lecture delves into the morphism of determinants and the determinant of matrices in block upper triangular form. Additionally, it discusses elementary operations on matrix columns, including transposition, dilation, and linear combination. The lecture concludes with the development of Lagrange's theorem for determinants along both rows and columns.