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Suppose f : Rn → Rm is a function such that each of its first-order partial derivatives exist on Rn. This function takes a point x ∈ Rn as input and produces the vector f(x) ∈ Rm as output. Then the Jacobian matrix of f is defined to be an m×n matrix, denoted by J, whose (i,j)th entry is � � � = ∂ � � ∂ � � {\texts tyle \mathbf {J} _{ij}={\frac {\partial f_{i}}{\partial x_{j}}}}, or explicitly � = [ ∂ � ∂ � 1 ⋯ ∂ � ∂ � � ] = [ ∇ T � 1 ⋮ ∇ T � �� � ] = [ ∂ � 1 ∂ � 1 ⋯ ∂ � 1 ∂ � � ⋮ ⋱ ⋮ ∂ � � ∂ � � 1 ⋯ ∂ � � � � � � ] {\displayst yle \mathbf {J} ={\begin{bmatrix}{\dfra c {\partial \mathbf {f} }{\partial x_{1}}}&\cdots &{\dfrac {\partial \mathbf {f} }{\partial x_{n}}}\end{bmatrix}}={ \begin{bmatrix}\nabla ^{\mathrm {T} }f_{1}\\\vdots \\\nabla ^{\mathrm {T} }f_{m}\end{bmatrix}}={\ begin{bmatrix}{\dfrac {\partial f_{1}}{\partial x_{1}}}&\cdots &{\dfrac {\partial f_{1}}{\partial x_{n}}}\\\vdots &\ddots &\vdots \\{\dfrac {\partial f_{m}}{\partial x_{1}}}&\cdots &{\dfrac {\partial f_{m}}{\partial x_{n}}}\end{bmatrix}}} where ∇ T � � {\displa ystyle \nabla ^{\mathrm {T} }f_{i}} is the transpose (row vector) of the gradient of the � i-th component.

imagine formal rushing 600 girls and ending up with less than 10... ugh. if that doesnt tell you enough about this chapter idk what will. the members dont care theyre not even friendly or welcoming. im dropping asap smd

such good recruiters this year. they dropped me but two of my suitemates went chi o and they love it so much. so kind, funny and outgoing. maybe COB

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