Jacobian

122. Jacobian

For a vector valued function

𝑔 (𝑥) = [\begin{matrix} 𝑔_{1} (𝑥) \\ 𝑔_{2} (𝑥) \\ ⋮ \\ 𝑔_{𝑚} (𝑥) \end{matrix}] 𝑔 : ℝ^{𝑛} \to ℝ^{𝑚}

The Jacobian:

𝐽_{𝑔} (𝑥) = [\begin{matrix} \nabla 𝑔_{1} {(𝑥)}^{𝑇} \\ \nabla 𝑔_{2} {(𝑥)}^{𝑇} \\ ⋮ \\ \nabla 𝑔_{𝑚} {(𝑥)}^{𝑇} \end{matrix}]