/sci/ - Science & Math

>>11120739
I sense opportunity

Hey /sci/, quick question on understanding a proof. I can DO the proof, I just don't quite understand the initial setup.

"If A is a symmetric matrix, then any two eigenvectors corresponding to distinct eigenvalues of A are orthogonal."
Let v1 and v2 be eigenvectors corresponding to the distinct eigenvalues λ1 =/= λ2, so that Av1 = λ1v1 and Av2 = λ2v2. Using A^T = A, and the fact that x . y = x^t . y for any two vectors....

To keep it quick I know the punch line is showing that λ1(v1 . v2) = λ2(v1 . v2), then subtracting to show that when you subtract the two to = 0, v1 and v2 have to be orthogonal. I just don't quite understand the setup of where we get the initial step of λ1(v1.v2) from, the (v1.v2) component. I'm not sure how we went from λ1.v1 to λ1(v1.v2)

It is probably pretty stupid, but sorta makes understanding why the proof works out well a little difficult. Thanks for the quick tip.

I think both are important in the grand scheme of things. It is okay to dedicate yourself fully to one or the other, but it is good to have a mix of them.

I'll be the first to admit that math, as beautiful as it is, can get stale. So it is nice to take a break and indulge in something else entirely. I'm trying to keep myself playing music on the side while I'm at college, just because it is a great hobby and I struggle to believe there are people who can only have one or the other.

Daily reminder you will never be a true patrician if you aren't well-rounded

>>4585486
No. That's not how IQ works. It is however true that IQ isn't everything, only a fool let's that stop him from achieving his goals. IQ != success, IQ + persistance = success.

Hey /sci/, what would happen if I cum in a syringe and inject it in my veins?

(2x + 4y) dx + (2x - 2y) dy = 0

the partial of M with respect to y = 4, N with respect to x = 2
therefore, the integrating factor is the exponential function to the integral of 1/x + 1/2y

My question is: how do I know which differential operator do I use? and why?

Hello /sci/

My name is John

OP, you forgot the prime directive.

inb4 trek-fag

>>1750292
I have had more memorable dreams than I have ever had sleeping monophasically. Remembering dreams > more dreams.
>>1750282
Interferes with my lounging around at lunch time. Instead of having beer at the local uni cafe I have to have a 20 minute nap. No one minds though when I leave and come back.
>>1750286
Not more powerful, but I do get a bit of time dilation.
>>1750291
Time dilation sometimes makes me loose track of what day it is. I often have to refer to a calendar. >>1750289
It makes me wonder why they are hitting the fire. Why would you hit fire?

I will have more hours in the day to study for my degree. I am studying from 4am until 7am every day. Thats 3 more hours of effective memorization before my nap.

Also I am doing it out of interest, for I think many people approach the Uberman cycle inefficiently. I would like to know if it is a viable lifestyle whilst strength training because if you can receive ample recovery from your mind whilst you are napping, and your body naturally heals whilst you are awake, then there is little or no point in sleeping for an entire 9 hours a night. Why waste life?

>>1639085
>mailto:rhizöme.döt.josef.at.googlemäil.dot.cöm
I'll try rhizome.josef@gmail.com

>>1562834

It seems to me that he has no intention in correcting or teaching her (which is the better approach imo) but only wants to bash the shit out of her

bump for a thread without trolls