# tatin

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 Name tatin Member for 6 months Seen yesterday Website Location Age 32
 Feb12 revised Subspace of Skew-symmetric Matrices of Rank Fouradded 7 characters in body Feb12 comment Subspace of Skew-symmetric Matrices of Rank FourYou are right. I'm referring to linear subspace. Let me modify the question so as to avoid the confusion. Feb12 revised A Question on Exterior Formsedited tags; edited title; edited tags Feb12 comment Subspace of Skew-symmetric Matrices of Rank FourI 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. Feb12 asked Subspace of Skew-symmetric Matrices of Rank Four Feb4 comment Non-negative Quadratic forms with Exterior FormsIt may have some some connection with the following thread: mathoverflow.net/questions/118037/… Jan4 asked On the Positive Definiteness of a Linear Combination of Matrices Dec18 comment Classical Derivative, Weak Derivative and Integration by PartsLet 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. Dec18 comment Classical Derivative, Weak Derivative and Integration by PartsI'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. Dec17 comment Classical Derivative, Weak Derivative and Integration by PartsThe way it is defined in the context of Sobolev spaces Dec17 awarded ● Critic Dec17 revised Classical Derivative, Weak Derivative and Integration by Partsadded 14 characters in body Dec17 asked Classical Derivative, Weak Derivative and Integration by Parts Dec5 revised PDE with the Jacobian Determinantadded 11 characters in body Dec5 comment PDE with the Jacobian Determinant@Robert Bryant: Thank you. Connectedness is an assumption here. Re-edited accordingly. Dec5 awarded ● Commentator Dec5 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. Dec5 revised PDE with the Jacobian Determinantadded 5 characters in body Dec4 revised PDE with the Jacobian Determinantadded 141 characters in body; edited title Dec4 asked PDE with the Jacobian Determinant Nov22 comment A Question on Exterior Forms@Sergei: Thank you. Very nice example!!. Nov21 comment A Question on Exterior FormsThanks a lot! I do not know how to thank you enough!!! Nov21 comment A Question on Exterior FormsThanks 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? Nov20 comment A Question on Exterior FormsI have modified so to avoid any confusion. Nov20 revised A Question on Exterior Formsadded 7 characters in body Nov20 comment A Question on Exterior FormsYes. A vector subspace. Nov20 comment A Question on Exterior FormsNote 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. Nov20 asked A Question on Exterior Forms Nov20 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?