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Jun
8
comment Prove that if A is singular, then adj(A) is also singular
You can prove directly that $\mathrm{adj}(A)=0$ if $A$'s rank is at most $n-2$ ($n$ is the size of the square matrix $A$), and $\mathrm{rk}(\mathrm{adj}(A))=0$ if $\mathrm{rk}(A)=n-1$.
Jun
8
comment finite dimensional CW complex
@Berci no, I forgot about that, fixed it.
Jun
8
comment finite dimensional CW complex
No, take for instance the CW complex with a single vertex and an infinite amount of two dimensional simplices, and no other simplices in any dimension.
Jun
7
comment Universal enveloping algebra of sl2
This looks alright, just use the fact that the $x^iy^jh^k$, $0\leq i,j,k$, form a basis (Poincaré-Birkhoff-Witt), and compare coefficients (in particular those coefficients with $i$ maximal).
Jun
7
comment Homotopy equivalence and chain complexes
What does you mean when you write "then $\phi$ is homotopic"? Do you mean "then $\phi$ is a homotopy equivalence"? On a side note, you can make your question more readable by quoting the actual exercise before quoting the theorem you want to use.
Jun
7
revised $A^2 B=A $ iff $B^2 A=B$
added 10 characters in body
Jun
7
comment Undergraduate Linear Algebra Problem
On a side note, there is a mock proof of this identity using power series. Once you see it, you can't forget about it!
Jun
7
answered $A^2 B=A $ iff $B^2 A=B$
Jun
6
comment Evaluate $\lim\limits_{n\to\infty}(1+x)(1+x^2)\cdots(1+x^{2n}),|x|<1$
$$\prod_{n=1}^\infty(1+x^n)$$ is the generating series for the partitions of integers into distinct parts.
Jun
5
comment canonical map of a monoid to its classifying space
Unless $M$ is discrete, the classifying space of $M$ will not coïncide with the classifying space of the one object category with morphisms $M$. A different construction is done for topological groups and is known under thename Milnor construction / Milnor Classifying space, and there are similar constructions for $H$-spaces due (I think) to Stascheff. In any case, my point is that the authors are likely using a different construction of the classifying space than that of the classifying space of the one object category with morphisms $M$.
Jun
5
comment canonical map of a monoid to its classifying space
Probably the unit of some adjunction, bar/cobar or something similar. That's what I'd guess.
Jun
4
comment If a Point Admits an Integral Curve on an Interval then a Neighborhood Does too On the Same Interval
It talks about $\Bbb R^2$, but I think that's an oversight, the french version of the page talks about continuous vector fields on $\Bbb R^n$ for arbitrary $n$.
Jun
4
answered Can there be a function holomorphic around $0$ w/ this property?
Jun
4
comment If a Point Admits an Integral Curve on an Interval then a Neighborhood Does too On the Same Interval
I think the Cauchy-Peano existence theorem takes care of existence of integral curves for any continuous vector field.
Jun
4
comment Looking For a Neat Proof of the Fact that the Grassmannian Manifold is Hausdorff
I asked a few very similar questions a few years ago, this question about shrinking group actions I asked with this exact calculation in mind.
Jun
3
comment Looking For a Neat Proof of the Fact that the Grassmannian Manifold is Hausdorff
"Disturbingly neat" ^^ oh really? But you're right, it's pretty mundane stuff.
Jun
3
comment Looking For a Neat Proof of the Fact that the Grassmannian Manifold is Hausdorff
Yes. ${}{}{}{}$
Jun
3
answered Looking For a Neat Proof of the Fact that the Grassmannian Manifold is Hausdorff
Jun
3
comment Finding the Jordan Canonical form of a $6 \times 6$ matrix
$A-I$ is nilpotent, it will most certainly not have the same rank as its square! You'll find that $(A-I)^2$ has all its coefficients zero, except for its last line which equals $$(\;4\quad 0\quad 0\quad 0\quad 0\quad 0\;)$$
Jun
1
comment Prove that $G = \langle x,y\ |\ x^2=y^2 \rangle $ is torsion free.
@Kaster $G$ won't be an abelian group, it's basically the set of words in $x,x^{-1},y,y^{-1}$ where each occurrence of $x^2$ may be replaced by $y^2$, and vice versa. Multiplication is by juxtaposition of words.