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3h
answered How do I show that $n=2$ is the only integer satisfy :$\cos^n\theta+ \sin^n\theta=1$ for all $\theta$ real or complex?
3h
answered Error with the proof that all solutions to the Cauchy Functional Equation are linear
1d
comment Countable Union of Countable Sets
How does the last part work? "We can easily show that every [countable] union of countable sets can easily be placed in a 1-1 and onto fashion with this specific union of countable set."
1d
reviewed Approve Countable Union of Countable Sets
1d
answered Row swapping through matrix multiplication
1d
answered Number of ways to separate $n$ points in the plane
2d
revised What does the ideal norm of matrix elements really mean?
another tag
Feb
3
comment Find the “surface neighborhood” of a point on a sphere for computer graphics
If so, see the accepted answer to this question: math.stackexchange.com/questions/56784/…
Feb
3
comment Find the “surface neighborhood” of a point on a sphere for computer graphics
So you want a function that, given a point $x$ on a sphere and a maximum distance $d$, returns a point sampled uniformly from within $d$ of $x$?
Feb
3
comment Find the “surface neighborhood” of a point on a sphere for computer graphics
What quantity, exactly, will your program need to compute? Do you need only a function that returns the distance between two points on a sphere? Or something more?
Feb
2
comment What does the ideal norm of matrix elements really mean?
@yoyo Sorry, I don't have any progress to report on this. I actually haven't thought about it much since asking the question, although I have vague plans to pick it up again someday. I'll be very interested if we do get an answer!
Jan
26
comment How to prove associativity of quaternion multiplication using scalar and vector form?
The dot product is not associative. First of all, it doesn't make sense to write a repeated dot product, since the dot product of two vectors is not a vector. But even if you interpret it as a scalar product, the value of $\hat x\cdot\hat x\cdot\hat y$ depends on the order of evaluation.
Jan
26
comment How to prove associativity of quaternion multiplication using scalar and vector form?
I'm not sure that this is the problem, but notice that you've written ${\bf{q}}\cdot{\bf{p}}\cdot{\bf{r}}$, which is ill-defined. Try being more careful with that, and see if it cancels anything else in the expression.
Jan
20
comment Proving additive inverse of vector set exists and “works”
@sinbadh Sure!!
Jan
20
comment Proving additive inverse of vector set exists and “works”
Great explanation! I would qualify what you wrote about $-(a,b)$. Since $V$ is a group but not a vector space, I think the most natural interpretation of that notation is "the additive inverse of $(a,b)$", which is precisely $(-a,-b)$. If $V$ were a vector space, this would equal $-1(a,b)$, but it isn't and it doesn't.
Jan
20
comment Proving additive inverse of vector set exists and “works”
(If you want to be really pedantic, you can mention that $-a_1$ and $-a_2$ exist and are unique as a consequence of the field axioms for $F$. But that is probably overkill for any reader, including your teacher.)
Jan
20
comment Proving additive inverse of vector set exists and “works”
@p3ngu1n Yep, that's it! Then, you'll want to prove that it really is the additive inverse by carrying out the definition of addition in $V$.
Jan
20
answered Proving additive inverse of vector set exists and “works”
Jan
15
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15
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