Derivative (Jacobian) of transposed functionJacobian of mappingJacobian for matrix function involving kronecker productWhat is the derivative of the ReLu of a Matrix with respect to a matrixJacobian of a matrix-valued functionWhen are functions related by transposed Jacobians?The product of the Jacobian and its transposed inverseUsing Jacobian insted of Lie DerivativeJacobian of two vectors and $fracpartialxpartial(xt)$Why is the Jacobian determinant of a map the reciprocal of the Jacobian determinant of the inverse map?Jacobian and Gradient Relation?
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Derivative (Jacobian) of transposed function
Jacobian of mappingJacobian for matrix function involving kronecker productWhat is the derivative of the ReLu of a Matrix with respect to a matrixJacobian of a matrix-valued functionWhen are functions related by transposed Jacobians?The product of the Jacobian and its transposed inverseUsing Jacobian insted of Lie DerivativeJacobian of two vectors and $fracpartialxpartial(xt)$Why is the Jacobian determinant of a map the reciprocal of the Jacobian determinant of the inverse map?Jacobian and Gradient Relation?
$begingroup$
Let $x in R^n$, $F in R^m times n$ and $f(x) = Fx$. It's easy to conclude that the Jacobian of $f(x)$ is $Df(x) = F$.
Where $Df(x)_ij = fracpartial f_ipartial x_j$.
Therefore $nabla f = (D f)^T $.
Now consider $g(x) = f(x)^T = x^TF^T$, what would $Dg(x)$ be?
Should I compute $Df(x)$ first and then simply take the transpose? But if I want to follow the definition of Jacobian ($Df(x)_ij = fracpartial f_ipartial x_j$), this way would break it completely. So what should the Jacobian be here?
matrices derivatives jacobian gradient-descent
asked Mar 20 at 17:57
huangzonghaohuangzonghao
558
$endgroup$
add a comment |
$begingroup$
Let $x in R^n$, $F in R^m times n$ and $f(x) = Fx$. It's easy to conclude that the Jacobian of $f(x)$ is $Df(x) = F$.
Where $Df(x)_ij = fracpartial f_ipartial x_j$.
Therefore $nabla f = (D f)^T $.
Now consider $g(x) = f(x)^T = x^TF^T$, what would $Dg(x)$ be?
Should I compute $Df(x)$ first and then simply take the transpose? But if I want to follow the definition of Jacobian ($Df(x)_ij = fracpartial f_ipartial x_j$), this way would break it completely. So what should the Jacobian be here?
matrices derivatives jacobian gradient-descent
asked Mar 20 at 17:57
huangzonghaohuangzonghao
558
$endgroup$
add a comment |
$begingroup$
Let $x in R^n$, $F in R^m times n$ and $f(x) = Fx$. It's easy to conclude that the Jacobian of $f(x)$ is $Df(x) = F$.
Where $Df(x)_ij = fracpartial f_ipartial x_j$.
Therefore $nabla f = (D f)^T $.
Now consider $g(x) = f(x)^T = x^TF^T$, what would $Dg(x)$ be?
Should I compute $Df(x)$ first and then simply take the transpose? But if I want to follow the definition of Jacobian ($Df(x)_ij = fracpartial f_ipartial x_j$), this way would break it completely. So what should the Jacobian be here?
matrices derivatives jacobian gradient-descent
asked Mar 20 at 17:57
huangzonghaohuangzonghao
558
$endgroup$
Let $x in R^n$, $F in R^m times n$ and $f(x) = Fx$. It's easy to conclude that the Jacobian of $f(x)$ is $Df(x) = F$.
Where $Df(x)_ij = fracpartial f_ipartial x_j$.
Therefore $nabla f = (D f)^T $.
Now consider $g(x) = f(x)^T = x^TF^T$, what would $Dg(x)$ be?
Should I compute $Df(x)$ first and then simply take the transpose? But if I want to follow the definition of Jacobian ($Df(x)_ij = fracpartial f_ipartial x_j$), this way would break it completely. So what should the Jacobian be here?
matrices derivatives jacobian gradient-descent
matrices derivatives jacobian gradient-descent
asked Mar 20 at 17:57
huangzonghaohuangzonghao
558
asked Mar 20 at 17:57
huangzonghaohuangzonghao
558
asked Mar 20 at 17:57
huangzonghaohuangzonghao
558
asked Mar 20 at 17:57
huangzonghaohuangzonghao
558
asked Mar 20 at 17:57
huangzonghaohuangzonghao
558
558
add a comment |
add a comment |
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