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Matrix Decompositions: LU, Cholesky, QR, Eigendecomposition
This lecture covers modern numerical linear algebra focusing on matrix and vector operations, LU decomposition, Cholesky decomposition, QR decomposition, and Eigendecomposition. The goal is to utilize matrix properties for problem-solving. The instructor explains the algorithms for LU decomposition, forward/backward substitution, and the computational complexity involved. Additionally, the lecture introduces the Lotka-Volterra equations for predator-prey interactions and their simulation. The session concludes with a discussion on Prey-Predator Cycles and real data analysis.