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visits member for 2 years, 7 months
seen Jul 24 at 17:13

Apr
30
asked Inducing orientations on boundary manifolds
Apr
27
accepted Probability that random vectors have a certain dot product
Apr
27
comment Probability that random vectors have a certain dot product
er, what i mean is that you are integrating with respect to the variable in the upper index. you need to make one of those variables different.
Apr
27
comment Probability that random vectors have a certain dot product
The upper index of your integral should be $\pi/2$, I think.
Apr
27
comment Probability that random vectors have a certain dot product
Yes, random unit vectors. Let me edit.
Apr
27
asked Probability that random vectors have a certain dot product
Apr
25
comment Why is Matrix Multiplication Not Defined Like This?
It is used sometimes. This is the dot product of two vectors, essentially. Sometimes you want to consider this dot product between two matrices. Matrix multiplication as defined usually allows you to compute the composition of linear functions.
Apr
25
comment Can you express nice manifolds as the zero locus of functions with linearly independent derivatives?
Thanks for helping me work through it. :)
Apr
25
answered Can you express nice manifolds as the zero locus of functions with linearly independent derivatives?
Apr
25
comment Can you express nice manifolds as the zero locus of functions with linearly independent derivatives?
I'm using that the columns of $[Df(x)]$ are the rows of $\nabla$.
Apr
25
comment Can you express nice manifolds as the zero locus of functions with linearly independent derivatives?
Ok, in my case the matrix $[Df(x)]$ is $(n-k)\times k$, with each column the $k$ partial derivatives. The onto condition is equivalent to asking that the rows be linearly independent, I think. Which is the same as asking that the $\nabla f_i$'s are linearly independent.
Apr
25
comment Can you express nice manifolds as the zero locus of functions with linearly independent derivatives?
@JasonDeVito, I'm confused actually. It's not true that $[Df(x)]$ is square. The onto condition should mean that the columns are linearly independent, no? Isn't this the conclusion that I require?
Apr
25
comment Can you express nice manifolds as the zero locus of functions with linearly independent derivatives?
Thank you, I knew I was probably being stupid about something. Make that an answer and I'll give it to you.
Apr
25
revised Can you express nice manifolds as the zero locus of functions with linearly independent derivatives?
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Apr
25
asked Can you express nice manifolds as the zero locus of functions with linearly independent derivatives?
Apr
15
accepted understanding simple multivariable integrals in terms of differential forms
Apr
15
asked understanding simple multivariable integrals in terms of differential forms
Mar
1
comment General questions about Eisenstein series and modular forms
This is a really nice answer. I'd greatly appreciate your recommendation for a good book on this stuff to go along with the previous suggestion. Maybe something to feel the big picture as well as the little details.
Mar
1
accepted General questions about Eisenstein series and modular forms
Feb
27
revised General questions about Eisenstein series and modular forms
added 33 characters in body