tatin
|
Registered User
|
|
|
Feb 12 |
revised |
Subspace of Skew-symmetric Matrices of Rank Four added 7 characters in body |
|
Feb 12 |
comment |
Subspace of Skew-symmetric Matrices of Rank Four You are right. I'm referring to linear subspace. Let me modify the question so as to avoid the confusion. |
|
Feb 12 |
revised |
A Question on Exterior Forms edited tags; edited title; edited tags |
|
Feb 12 |
comment |
Subspace of Skew-symmetric Matrices of Rank Four I do not understand one point. You mentioned that $E_4(5)=10$. Let us take $S:=e_1\wedge\mathbb{R}^5$. Then, S is a subspace of $5\times 5$ skew-symmetric matrices that has trivial intersection with $E_4(5)$. This implies that dimension of $E_4(5)$ has to be less than or equal to 10-4=6. |
|
Feb 12 |
asked | Subspace of Skew-symmetric Matrices of Rank Four |
|
Feb 4 |
comment |
Non-negative Quadratic forms with Exterior Forms It may have some some connection with the following thread: mathoverflow.net/questions/118037/… |
|
Jan 4 |
asked | On the Positive Definiteness of a Linear Combination of Matrices |
|
Dec 18 |
comment |
Classical Derivative, Weak Derivative and Integration by Parts Let me say it again: I'm sorry for the confusion. I have had the impression that the term "weak derivative" is used when the distributional derivative is a $L^1_{loc}$ function. I thought that this is a standard convention but, as it seems, I'm wrong. |
|
Dec 18 |
comment |
Classical Derivative, Weak Derivative and Integration by Parts I'm sorry for the confusion. I have had the impression that the term "weak derivative" is used when the distributional derivative is a $L^1_{loc}$ function. I thought that this is a standard convention but, as it seems, I'm wrong. |
|
Dec 17 |
comment |
Classical Derivative, Weak Derivative and Integration by Parts The way it is defined in the context of Sobolev spaces |
|
Dec 17 |
awarded | ● Critic |
|
Dec 17 |
revised |
Classical Derivative, Weak Derivative and Integration by Parts added 14 characters in body |
|
Dec 17 |
asked | Classical Derivative, Weak Derivative and Integration by Parts |
|
Dec 5 |
revised |
PDE with the Jacobian Determinant added 11 characters in body |
|
Dec 5 |
comment |
PDE with the Jacobian Determinant @Robert Bryant: Thank you. Connectedness is an assumption here. Re-edited accordingly. |
|
Dec 5 |
awarded | ● Commentator |
|
Dec 5 |
comment |
PDE with the Jacobian Determinant @Ryan budney: What you are talking about is the problem with prescribed divergence which is essentially the linearized version of the problem with prescribed Jacobian. |
|
Dec 5 |
revised |
PDE with the Jacobian Determinant added 5 characters in body |
|
Dec 4 |
revised |
PDE with the Jacobian Determinant added 141 characters in body; edited title |
|
Dec 4 |
asked | PDE with the Jacobian Determinant |
|
Nov 22 |
comment |
A Question on Exterior Forms @Sergei: Thank you. Very nice example!!. |
|
Nov 21 |
comment |
A Question on Exterior Forms Thanks a lot! I do not know how to thank you enough!!! |
|
Nov 21 |
comment |
A Question on Exterior Forms Thanks again. Thank a lot. I'm not familiar with representation theory. It will take me some time to understand your counterexample fully. Is there any direct counterexample that constructs the subspace explicitly? |
|
Nov 20 |
comment |
A Question on Exterior Forms I have modified so to avoid any confusion. |
|
Nov 20 |
revised |
A Question on Exterior Forms added 7 characters in body |
|
Nov 20 |
comment |
A Question on Exterior Forms Yes. A vector subspace. |
|
Nov 20 |
comment |
A Question on Exterior Forms Note that, your example is not the right one. For $\omega_{+}$,$\omega_{-}$ both cannot be in $N$ as $\omega_{+}+\omega_{-}=2dx_1\wedge dy_1$ which is decomposable whereas $N$ cannot contain non-zero decomposable forms. |
|
Nov 20 |
asked | A Question on Exterior Forms |
|
Nov 20 |
comment |
Inequalities Involving Wedge Product (Reference Request) Unfortunately, we do not have the linear independence of $\omega_1^2, \omega_2^2$ and $\omega_1\wedge \omega_2^2$. What we have is that $$ (\alpha\omega_1+\beta\omega_2)^2\neq 0,\text{ for all }\alpha,\beta\neq 0. $$ In this case, is there any way to guaranty that the open set passes through the region? |
