The Hessian of a function (denoted $ F(x_1, x_2, \cdots , x_n) $) is the multivariate equivalent to the second derivative of a single variable function. Similar to the Gradient of a multivariate function, the Hessian is a square matrix where each entry is the composite of two partial differentiations. For a function $ f(x_1, x_2, \cdots , x_n) $, the Hessian is defined as:
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