2nd Order Taylor Series Formula inv. the Hessian Matrix, etc. - what is the x vector?

by jaguar7
Tags: formula, hessian, matrix, order, series, taylor, vector
 Math Emeritus Sci Advisor Thanks PF Gold P: 39,353 x is the vector . And you need a quadratic in the second term- it should be $$f(a, b)+ \begin{bmatrix}\frac{\partial f}{\partial x}(a, b) & \frac{\partial f}{\partial y}(a, b)\end{bmatrix}\begin{bmatrix}x- a \\ y- b\end{bmatrix}+ \frac{1}{2}\begin{bmatrix}x- a & y- b\end{bmatrix}\begin{bmatrix}\frac{\partial^2 f}{\partial x^2}(a,b) & \frac{\partial^2 f}{\partial x\partial y}(a,b) \\ \frac{\partial^2 f}{\partial x\partial y}(a,b) & \frac{\partial^2 f}{\partial y^2}(a,b)\end{bmatrix}\begin{bmatrix} x- a \\ y- b\end{bmatrix}$$