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Mar
13
comment Definition of critical point
I think I'm confused about the definition of $df_p$. In my textbook, it seems $df_p$ is the derivative--I'm probably wrong on this, but I have this impression because it can be written as Jacobian matrix.
Mar
13
comment Definition of critical point
Thanks! Yes, the space spanned by $df_p=1$ is $\mathbb{R}$, but that's not equivalent to $df_p$ being surjective?
Mar
13
comment Definition of critical point
Suppose $df_p=1$. Why is this surjective?
Mar
13
comment Definition of critical point
Can I ask the reason why "Since its codomain is 1-dimensional, dfp is either surjective or the zero map"?
Mar
13
comment Definition of critical point
Sorry that I don't understand your explanation... If at a regular point the differential fails to be surjective, then there'd be something wrong with the definition?!
Mar
13
asked Definition of critical point
Mar
5
accepted Definition of operator norm
Mar
5
asked Definition of operator norm
Feb
12
revised How to show augmentation ideal is an ideal
edited tags
Feb
12
asked How to show augmentation ideal is an ideal
Jan
31
accepted Is simple module over commutative ring always a field?
Jan
31
comment Is simple module over commutative ring always a field?
But after defining this multiplication in $M$, why doesn't this make $M$ a field? Still confused about the logic...
Jan
31
comment Is simple module over commutative ring always a field?
I'm still confused--why can I treat $M$ as a ring by transferring the structure of $R/I$ if it's not actually a ring?
Jan
31
asked Is simple module over commutative ring always a field?
Jan
30
comment Non-analytic smooth function
@MarianoSuárez-Alvarez If a real analytic function is 0 in an open set in $\mathbb{R}$, can I say it's 0 on the whole real line by this argument?
Jan
30
asked Non-analytic smooth function
Jan
30
awarded  Yearling
Jan
30
revised $Rx$ is a simple module
deleted 149 characters in body
Jan
30
accepted $Rx$ is a simple module
Jan
30
awarded  Custodian