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Aug
30
comment If $N$ is nilpotent of index $n\geq 2$ but $N^{n-1}\neq 0$ then there's no $A$ such that $A^2=N$
Looks good. You can also deduce a contradiction by noticing that $A$ must be nilpotent and considering the possible indices of nilpotency of $A$.
Aug
30
answered If $N$ is nilpotent then there exists $A$ such that $A^2=I+N$
Aug
30
revised Simultaneous orthogonal diagonalization of two matrices
fixed a typo
Aug
30
comment $GL_n(\mathbb{C})$-conjugation invariant $\mathbb{C}$-valued polynomial has certain form.
math.stackexchange.com/questions/78065/…
Aug
30
answered Are vectors $e_i$ linearly independent if and only if the matrix $A$ is nonsingular?
Aug
29
comment Differential geometry: restriction of differentiable map to regular surface is differentiable
You need to choose $U_1$ small enough such that $\varphi(\mathbf{x}_1((U_1)) \subseteq M$ and then you don't need to restrict $\mathbf{x}_2^{-1}$.
Aug
29
revised Simultaneous orthogonal diagonalization of two matrices
added 227 characters in body
Aug
29
answered Simultaneous orthogonal diagonalization of two matrices
Aug
26
comment Differential geometry: restriction of differentiable map to regular surface is differentiable
$\mathbf{x}_2(U_2)$ is an open subset of the regular surface $S_2$, while $M$ is an open subset of $\mathbb{R}^3$. The intersection is an open subset of $S_2$ but not an open subset of $\mathbb{R}^3$.
Aug
25
answered Unitary matrix and Spherical Symmetry
Aug
25
comment Differential geometry: restriction of differentiable map to regular surface is differentiable
Looks good. Note that you don't want to restrict $\tilde{\mathbf{x}}_2^{-1}$ to $N$ because $N$ is not an open subset of $\mathbb{R}^3$ and then you can't use the regular chain rule. Also, you need to make the open subset on which $\mathbf{x}_1$ is defined possibly smaller so that the image of $\varphi \circ \mathbf{x}_1$ will land in $M$.
Aug
23
answered Differential geometry: restriction of differentiable map to regular surface is differentiable
Aug
18
reviewed Approve Max volume of a cuboid given constraint
Aug
18
revised Proving that given any two points in a connected manifold, there exists a diffeomorphism taking one to the other
latex formatting
Aug
18
comment Relationship between isomorphic vector spaces and inner product
"pushfoward" is just a name (because you take an inner product on $V$ and using $\phi \colon V \rightarrow W$, push it foward to an inner product on $W$) for the construction I described in the answer. You're welcome!
Aug
18
answered Relationship between isomorphic vector spaces and inner product
Aug
18
revised Rigorous meaning of the expression $dz = dx + idy$
latex formatting
Aug
10
revised Show that a subset is a submanifold of $ \mathbb{R}^4$
formatting, spelling
Aug
10
answered Metric Isometry is always smooth?
Aug
4
awarded  differential-geometry