A bordered Hessian matrix consists of the Hessian of a multivariate function f, and the gradient of a multivariate function g.
The gradient of a scalar field is a vector field which points in the direction of the greatest rate of increase of the scalar field, and of which the magnitude is the greatest rate of change.
The gradient function, g(x), evaluates the gradient of a real scalar function f at a point x.
The Hessian matrix is the square matrix of the second-order partial derivatives of a multivariate function.
The Hessian function, H(x), evaluates the Hessian of a real scalar function f at a point x.
The Jacobian matrix is the matrix of all first-order partial derivatives of a vector-valued function.
The Jacobian function, J(x), evaluates the Jacobian of a real vector-valued function f at a point x.
A partial derivative of a multivariate function is the derivative with respect to one of the variables with the others held constant.
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