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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?
added 231 characters in body
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?
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Oct
12
answered Is differentiating on both sides of an equation allowed?
Jul
9
awarded  Popular Question
Jun
12
comment What is the difference between Gödel's Completeness and Incompleteness Theorems?
Is there actually a name for a first-order-theory that is recursively enumerable, consistent and capable of arithmetic? If not, why not? Wouldn't that be a useful terminological distinction?
Jun
8
comment Are the Gödel's incompleteness theorems valid for both classical and intuitionistic logic?
@PeterSmith I guess they refer to the infinite set of natural numbers. Would arithmetic on a set of natural numbers with a highest number (ultrafinitism) be complete?