14 сент. 2018 г. · Let use the definition by differential. f(x0+Δx)=f(x0)+f′(x0)Δx+o(Δx). and by f(x)=Ax. A(x0+Δx)=Ax0+AΔx. therefore f′(x)=A.

5 дек. 2016 г. · In index notation yi=Ainxndyi=dAinxn∂yi∂Ajk=δijδnkxn=δijxk. You could write this result using the dyadic (⋆) product ∂y∂A=I⋆x.

29 нояб. 2021 г. · Let function f:R3×2→R3 be defined by f(A):=Ax. Compute the derivative of f with respect to A.

26 июн. 2019 г. · The Jacobian should be the map A itself, but the gradient is the Jacobian transpose, so we should have ∇(Ax)=AT.

21 февр. 2020 г. · Let A be a matrix of size n×n and x a n×1 vector. Consider y=x′AA′x, where y is a scalar. I want to compute the derivatives of y with respect to ...

6 февр. 2011 г. · Given a matrix A and column vector x, what is the derivative of Ax with respect to xT i.e. d(Ax)d(xT), where xT is the transpose of x? Side note ...

15 нояб. 2023 г. · We can compute the derivative directly using the chain rule: ∂∂aijg(Ax)=∑kgyk(Ax)∂∂aij∑ℓakℓxℓ=∑kgyk(Ax)δikxj=gyi(Ax)xj.

10 янв. 2021 г. · This derivative comes up in the differentiation of the euclidean norm and I can't seem to find an appropriate rule to apply that the dimensions match.

23 февр. 2013 г. · What does it mean formally to differentiate a function with respect to another function? 1 · Differentiating a matrix with respect to a vector.

18 февр. 2013 г. · You mean G(x)=F(Ax). This can't be, these are two different things. Like f′(2x) is not the derivative of f(2x).