Linear Programming 42: Totally unimodular matrices

Linear Programming 42: Totally unimodular matrices Abstract: We define and explain totally unimodular matrices. We prove the main theorem about totally unimodular matrices in linear programming, which states that if a linear programming problem has a totally unimodular constraint matrix, an integral constraint vector, and an optimal solution, then there necessarily also exists an integral optimal solution. This video accompanies the class "Linear Programming and Network Flows" at Colorado State University https://www.math.colostate.edu/~adams/teaching/math510fall2020/ We are following the book "Understanding and Using Linear Programming" by Jirí Matoušek and Bernd Gärtner https://link.springer.com/book/10.1007/978-3-540-30717-4 Our course notes are available at https://www.math.colostate.edu/~adams/teaching/math510fall2020/LinearProgrammingNotes.pdf