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Feb
24
comment Bilinear forms in ${\Bbb R}^3$
In $\Bbb{R}^3$, starting from $e_1$ and $e_2$, one gets $e_1x$ and $e_2x$ being perpendicular to each other. Then we have $x$ and $L^{-1}_{e_1}(e_2x)$, which give a tangent vector field $x\mapsto L^{-1}_{e_1}(e_2x)$. So $e_3$ is not needed?
Feb
24
comment Bilinear forms in ${\Bbb R}^3$
I don't quite follow your comment. What's more, it seems that one only needs an argument of $e_1x$ and $e_2x$. Would you explain why we need $e_3x$ also?
Feb
16
accepted Bilinear forms in ${\Bbb R}^3$
Feb
16
comment Bilinear forms in ${\Bbb R}^3$
Thank you for your answer! Where is the norm algebra in ${\Bbb R}^2$ from? Looks like the determinant of some matrix.
Feb
16
asked Bilinear forms in ${\Bbb R}^3$
Oct
27
comment Questions about Lyapunov functions
How can one get $4|x|\cdot|y|$ in the last estimate?
Jul
2
awarded  Curious
Dec
30
awarded  Commentator
Dec
30
comment Property of critical point when the Hessian is degenerate
I don't see why @user1938185's answer contradicts your argument that $(0,0)$ is not a local minimum.
Dec
30
comment Property of critical point when the Hessian is degenerate
According to your answer, it is a minimum?
Dec
30
asked Property of critical point when the Hessian is degenerate
Dec
30
revised Zero Eigenvalues for Hessian Matrix
Formula format correction
Dec
30
suggested approved edit on Zero Eigenvalues for Hessian Matrix
Oct
14
awarded  Yearling
Jan
25
answered Understanding of the residue $\operatorname{Res}(z_0,f)$
Jan
7
answered Inner regularity of Lebesgue measurable sets
Jan
7
comment Inner regularity of Lebesgue measurable sets
It is the measure that is bounded by $\varepsilon$. I think his question in comment is how you get the $K\subset E$ that is closed and bounded.
Jan
4
answered equivalence of measurability
Nov
11
comment Uniform convergence of $x^n$ on $(-1,1)$.
The point wise limit is $0$. Calculate $\lim_{n\to\infty}\|f_n\|$.
Nov
10
accepted Convergence of $\int_{0}^{+\infty}f(x)dx$