Jacobi matrix雅克比矩阵

cite from wikipedia

Vector calculus

Vector-by-vector

Each of the previous two cases can be considered as an application of the derivative of a vector with respect to a vector, using a vector of size one appropriately. Similarly we will find that the derivatives involving matrices will reduce to derivatives involving vectors in a corresponding way.

The derivative of a vector function (a vector whose components are functions) , of an independent vector , is written (in numerator layout notation) as

In vector calculus, the derivative of a vector function y with respect to a vector x whose components represent a space is known as the pushforward or differential, or the Jacobian matrix.

The pushforward along a vector function f with respect to vector v in R^m is given by 

在向量微积分中，向量函数y关于x(x的元素代表空间)的导数被认为是雅克比矩阵