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Jul
23
comment In manifold theory, in what sense is the derivative a first-order approximation?
The concept that is precisely generalized is "linear approximation". Namely, the differential of a function induces uniquely a linear map between tangent vectors, which in familiar contexts is exactly the first order approximation.
Jul
20
comment Natural bilinear map $B\colon Alt^p(E^*)\times Alt^p(E)\rightarrow\mathbb R$
Oh, ok, I get it.
Jul
20
answered Textbooks for self-study on general relativity?
Jul
15
reviewed Approve Given a corner, draw a square of known size minimizing vertex distance to a point
Jul
10
awarded  Nice Answer
Jul
8
answered Conditional probability ordering singers
Jul
8
awarded  Custodian
Jul
8
comment A product version of Riemann integral
You are welcome!
Jul
8
comment A product version of Riemann integral
Sure. Edited :)
Jul
8
revised A product version of Riemann integral
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Jul
8
answered A product version of Riemann integral
Jul
6
revised $A^tA-AA^t$ in Mathematical Physics
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Jul
6
comment $A^tA-AA^t$ in Mathematical Physics
Yes! In particular, $A^tA$ has a metric significance, it gives the length (for vectors), or metric tensors, or first fundamental forms. I'm asking exactly what the difference measures, though. Anyway your answer suggested me an edit, so thank you!
Jul
6
asked $A^tA-AA^t$ in Mathematical Physics
Jul
3
answered Is a principal bundle automorphism locally given by a left action?
Jul
3
answered (Co)Tangent bundle of Cone manifold
Jul
3
revised cross product of vector and direction
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Jul
3
answered The Euclidean Metric on $\mathbf R^3$ Induces an Index-Lowering Isomorphism $b:\mathfrak X(\mathbf R^3)\to \Omega^1(\mathbf R^3)$.
Jul
3
comment cross product of vector and direction
Actually this is circular, because the $Z$ direction is chosen exactly so that $\vec z = \vec x \times \vec y$ (it uses a cross product!), which implies what you say.
Jul
3
answered cross product of vector and direction