Rank Revisited: Line and Column

This lecture revisits the concepts of line rank and column rank in the context of matrices and linear applications. It explains how the line rank of a matrix is the dimension of the vector space spanned by its rows, while the column rank is the dimension of the vector space spanned by its columns. The lecture also covers the relationship between line and column ranks, illustrating with examples and theorems. It demonstrates how the column rank of a matrix is equal to its line rank, providing proofs and insights into the properties of linear transformations. Additionally, it explores the calculation of line ranks through examples of echelon matrices.