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 Tumbleweed
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Mar
21
revised How can I calculate the partial derivative $\frac{\partial}{\partial \vec{x}} f\left(A\vec{x} + \vec{b}\right)$ using matrix calculus?
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Mar
21
asked How can I calculate the partial derivative $\frac{\partial}{\partial \vec{x}} f\left(A\vec{x} + \vec{b}\right)$ using matrix calculus?
Feb
20
awarded  Tumbleweed
Feb
13
asked Why can I plug the roots of a partial derivative of a linear optimization objective E into E without changing it?
Jan
5
comment What is the geometric interpretation of the transpose?
"The action of a symmetric matrix can be regarded as a rotation to a new basis": I am confused by this statement. Rotation matrices don't have any eigenvectors and symmetric matrices have orthogonal eigenvectors, hence a symmetric matrix cannot be a rotation matrix.
Nov
10
comment Why is $\frac{d f(g(h(x)))}{d x} = \frac{d f(g(h(x)))}{d h(x)}\frac{d h(x)}{d x}$, not $\frac{d f(g(h(x)))}{d g(h(x)))}\frac{d h(x)}{d x}$?
Ah, I missed that I should identify the outer part with $f$. Am I right with the observation that the notation $(f(g(x)))' = f'(g(x))g'(x)$ completely obscures that $f'(g(x))$ is the derivative of $f$ wrt. $g(x)$ (not wrt. $x$).
Nov
10
accepted Why is $\frac{d f(g(h(x)))}{d x} = \frac{d f(g(h(x)))}{d h(x)}\frac{d h(x)}{d x}$, not $\frac{d f(g(h(x)))}{d g(h(x)))}\frac{d h(x)}{d x}$?
Nov
9
asked Why is $\frac{d f(g(h(x)))}{d x} = \frac{d f(g(h(x)))}{d h(x)}\frac{d h(x)}{d x}$, not $\frac{d f(g(h(x)))}{d g(h(x)))}\frac{d h(x)}{d x}$?
Nov
1
comment Combining Two Gaussian Filters
Hint: Fourier transform of convolution.
Oct
12
revised Is differentiating on both sides of an equation allowed?
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Oct
12
revised Is differentiating on both sides of an equation allowed?
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Oct
12
comment Is differentiating on both sides of an equation allowed?
@skyking You are right, I’ve corrected my answer. More precisely it means "find all assignments for $x$ such that…".
Oct
12
revised Is differentiating on both sides of an equation allowed?
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Oct
12
comment Is differentiating on both sides of an equation allowed?
Also note that the implication in the other direction in your last sentence is not true. For example if $f(x)=x$, $g(x)=2x$, then $f(x)≠g(x)$, but $f''(x)=g''(x)$.
Oct
12
revised Is differentiating on both sides of an equation allowed?
deleted 45 characters in body
Oct
12
revised Is differentiating on both sides of an equation allowed?
deleted 45 characters in body
Oct
12
revised Is differentiating on both sides of an equation allowed?
deleted 45 characters in body
Oct
12
comment Is differentiating on both sides of an equation allowed?
This answer is imprecise and incomplete, as 25 is also a function of x, a constant one, and there are other special cases in which differentiating both sides works.
Oct
12
comment Is differentiating on both sides of an equation allowed?
I partly agree, but my approach is also valid. The questions is where you want to hide the complexity, whether in the equal sign predicate or in the way you do the variable evaluation. I would tend to hide it in the equal sign though, but I’m not closely familiar for the common ways this is axiomatized.
Oct
12
revised Is differentiating on both sides of an equation allowed?
added 88 characters in body