Complex Hessian Equations: These are equations involving the Hessian matrix, which is a square matrix of second-order partial derivatives of a function. In complex analysis, these equations help ...

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Modern applications such as machine learning and large-scale optimization require the next big step, "matrix calculus" and calculus on arbitrary vector spaces. This class covers a coherent approach to ...

Another complication arises when the Jacobian matrix becomes nearly singular, which occurs near the intersection. This situation defines a bifurcation point (14) in the amplitude equations, leading to ...