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Jul
21
reviewed Reject Get amount of submatrixes from $a \times b $matrix
Jul
21
reviewed Reject How is the derivative geometrically inverse of integral?
Jul
20
comment Push-forward of vector fields by local isometries
Thanks for this answer, I'm hoping to guide a promising student through the Smooth Manifolds book next year, this helps!
Jul
20
revised Push-forward of vector fields by local isometries
added 4 characters in body
Jul
20
answered Push-forward of vector fields by local isometries
Jul
20
comment Push-forward of vector fields by local isometries
I would assume that the key word here is "local". We know for a local isometry the map $\phi$ is regular (meaning the local coordinate representative has full rank) hence $\phi$ suitably restricted gives a diffeomorphism from an open set $\mathcal{U}$ to another corresponding open set $\mathcal{V} = \phi (\mathcal{U})$. This is the inverse function theorem for manifolds.
Jul
20
comment How to see that SL(2,C) is simply connected?
Well, now answering (2.) is easy, $M$ is simply connected because $\text{Sl}(2, \mathbb{C})$ is simply connected ;)
Jul
18
reviewed Approve Proof question: Prove that 2^(odd integer) + 5^(odd integer) + 2 is a multiple of 3, and 4^(any integer) + 1 can be expressed as 5n, 5n + 1 or 5n + 2.
Jul
18
reviewed Reject Maths Puzzle: Partitioning a set into two disjoint sets
Jul
17
revised Can the following tensors be contracted?
name mispelt
Jul
17
revised Natural Coordinate Functions
name mispelt
Jul
17
comment Continuous map $\mathbb{R}^n\rightarrow\mathbb{R}^n$
math.stackexchange.com/questions/57686/… gives you a bit in the direction of understanding that differing norms on a finite dimensional topological space (like $\mathbb{R}^n$) give equivalent topologies and hence limits. Also, see page 67-68 of supermath.info/AdvancedCalculus13.pdf
Jul
15
comment “Grouping” differential equations and the appropriate methods for solving them
Very well then, you'll see them soon enough. Best wishes on your exam.
Jul
15
comment “Grouping” differential equations and the appropriate methods for solving them
you're missing exact equations. Maybe this wasn't covered yet?
Jul
15
reviewed Approve Giving two equal line segments AC and BD so that they bisect each other at E. Prove that quadrilateral ABCD is a Rectangle.
Jul
15
comment Proving that $\vec F=yz(2x+y+z)\hat i+zx(x+2y+z)\hat j+xy(x+y+2z)\hat k$ is conservative field
why not just find $U$ for which $\vec{F}= \nabla U$ then it is immediately true that $\nabla \times \nabla U=0$ and you have the potential to boot.
Jul
15
comment Isn't this article in wikipedia wrong? (Multilinear form)
on page 350 of Jacobson's Basic Algebra I he says there is a distinction between alternate and skew-symmetric. In particular, to show skew-symmetric implies alternate he notes: $b(x,x)=-b(x,x)$ implies $2b(x,x)=0$( which fails to prove $b(x,x)=0$ in the characteristic two case). Nevermind, I see you appreciate this point already and Jacobson agrees with your conclusion about the other direction.
Jul
14
reviewed Approve Evaluate$\int_{-2}^2\int_{y^2-3}^{5-y^2}dxdy$
Jul
14
reviewed Approve Finding all groups of order $7$ up to isomorphism?
Jul
14
comment Example tensor representation
Thanks! I hope you have more questions, these are fun.