@Alizter Implemented quartics into my program, and I'm able to give it $a\cdot x^4+b\cdot x^3+c\cdot x^2+d\cdot x+e$ just fine, it gives me a huge output though
@anon actually I use laplace transform to find it, since their definition are very close to each other. but I have a problem about how to convert it to PDF again?
wait, so originally you asked how to find the MGF from the PDF, then you tell me you already can find the MGF using the laplace transform, and your real question is how to get the PDF from the MGF with mathematica?
@anon I have Rayleigh fading channel, (in communication system), I can find the PDF of the overall system, but the problem there are convolution operator between each term, so I convert it to MGF, after manupulation I want to convert back to PDF for the purpose of Outage probability calculation
my integration by parts integral for $\int_0^\infty \! e^{-sx}sin(ax) \, \mathrm{d}x.$ is a mess. I got the result of $\frac{a}{a^2+s^2}$, but I think I'm missing something on my paper. Can I scan it and post it here?
@AlecTeal Community wiki means a post is intended to be collaboratively edited more than usual, and doesn't generate rep. Sometimes it's just CW'ed to make it rep-neutral. And moving answers to comments is something only moderators can do. Why do you ask?
@AlecTeal you tell an answerer (Will Jagy) to move a hint to a comment within mere minutes of seeing the response, even when you admit you don't understand how it helps? this seems very arrogant to me.
@anon @DanielFischer I think if it's a sentence that ought to be a comment, very verbose hints = answer material. math.stackexchange.com/questions/578614/… as I mention in the question I want to do it by definitions, we know only 3 things about <,> and I don't want to use inequalities with determinants.
Because that'd be very hard to do, it's not the size of elements of a matrix that matters really.
I thought there was some row operation I'd missed, so I tried to manipulate the definition of linearly dependent without success.
(because I'm not sure how to "say it", it means there are non-zero 'coordinates' such that the vector is zero, row operations looked promising)
BUT now it has an answer I am unlikely to see another.
I think what DF is getting at is that the gram matrix is symmetric if V is real, but is only hermitian if V is complex, because inner products have conjugate-symmetry
@DanielFischer I'd not considered that, I'm going to mess around on paper a sec, I'm sorry I can't answer. I hope this is a better response than me going quiet.
@anon I really don't want to use the Gram-ness(?) of the matrix, I believe (see the speculation part and the bit about the Schwarz inequality) that it should be true purely from definitions.
I can see no obvious route from definitions to the whole $A^TA$ thing, because of multiplication of <,> and without introducing inequalities by using the triangle inequality.
So while it is true, I am actively trying to avoid it.
Hello guys, I've spend my entire day trying to prove the following but no result: I need to show that $\delta \in H_s(\mathbb{R}^d)$ if and only if $s < -d/2$. The $H_s$ space is the $L^2$ Sobolev space, ie $$H_s = \{ f \in L^2 | \int |\hat{f}|^2 (1 + |\xi|^2)^s < \infty$$ I may have butchered that definition, so please correct me if I am wrong.
Your first line should be $\frac{a}{s^2} - \frac{a^2}{s^2} I = I$ Multiplying everything by $s^2$ gives $a - a^2 I = s^2 I$ so $a = (a^2 + s^2) I$. Dividing both sides by $a^2+s^2$ finishes the calculations. Seems you have to brush up on some of your algebra =)
@DanielFischer my searching brought up a book called Linear Algebra by a guy called Serge Lang, it's popping up a lot so I'm going to go get myself a copy from the library, BB in like 14 minutes, I've check it's there.
I can't help it if the school is that stupid to not list Math 321 and Math 311 as a recommended prep choice for 302 which is differential equations what I"m taking nao
It's the proof parts that drive me nuts, but at least I attempt it and not give up which is the worse thing to do
Keep going at it and it will soon feel very natural. Latex is to me as a second language after writing what I estimate to ble close to 100k lines of it in various projects.
These are mainly computations than proofs per say. There is a very fine line, but in my eyes a computation is where you have a clear path, it might be a tough one but clear nonetheless.
like how is it possible for a undergrad senior like me to be in a 400 level English course but only at a 300 level Math course? Something is fishy here.
@usukidoll Let $$ f(x+1) = \frac{1}{2}f(x) \, \forall x \in [0,3] \qquad \int_0^1 f(x) \mathrm{d}x= 1 $$ Find $$ \int_0^3 f(x)\mathrm{d}x $$ This should be a fun problem for you. Relatively simple.
@AlexanderGruber A vector space is a particular kind of module, and perhaps some intuition can come from there. But in my limited experience a lot of module theory is spent working outside of the modules themselves and instead with the category.
