Linear Systems: LU Factorization with Pivoting

This lecture covers the Gaussian elimination algorithm with pivoting for solving linear systems. It explains the importance of pivoting even when the diagonal element is not zero, and how to choose the pivot. The lecture also discusses the LU factorization with pivoting, the use of permutation matrices, and the factorization of a matrix into a product of lower and upper triangular matrices. The instructor demonstrates the algorithm step by step and provides practical insights on implementing it in Python.