Optimization and Dynamical Systems

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Focusing on advanced engineering applications, this work addresses optimization and linear systems theory through the lens of linear algebra, dynamical systems, and differential geometry. It covers essential topics such as matrix diagonalization, singular value decomposition, and linear programming, employing both continuous and discrete time dynamical systems for solutions. The research highlights recent breakthroughs in geometric invariant theory, providing insights into matrix least squares optimization problems that resist traditional algebraic approaches.