I feel bad lol. I had the same idea as InteGrand, I just mucked up my matlab input when I went to check my answer
_______________
This one's a bit long...
Proven in i): 0 is the only eigenvalue of B (so B is nilpotent)
Oh of course. Once I drew out the Jordan chain again and looked carefully at what the question gave iii made sense.
_________________________________________
Tools permitted if useful: Binomial theorem for matrices that commute in multiplication, Cayley-Hamilton theorem
Edit: Thanks IG I just saw where your reply was :P
Last edited by leehuan; 14 Jun 2017 at 9:11 PM.
No more questions for this sem after tomorrow.
__________________
This is a highly open-ended question and everyone's opinion might be different.
What's the easiest proof (or would be a very easy proof) of the Cauchy-Schwarz inequality to memorise?
Well you wrote one up here before, so maybe you'd find that easiest to "memorise" for yourself:
Note that it needs to be adapted slightly to deal with the complex case, but it's not too big a deal.
You can also probably find many proofs online. There are twelve proofs here, but they seem to only be for the case of R^n: http://www.uni-miskolc.hu/~matsefi/O...rticle1_19.pdf .
Completely forgot about that one.
_________________
Last edited by leehuan; 23 Jun 2017 at 8:29 PM.
This is just some personal fun
Last edited by leehuan; 19 Jul 2017 at 6:39 PM. Reason: Oh right, my bad
Hopefully you don't mind if i post a question here. (taking MATH2601 this semester)
Suppose that G is a group with precisely three distinct elements e (the identity), a and b.
a) Prove that ab = e (Hint: eliminate other possibilities).
b) Prove that a^2 = b.
c) Deduce that G = {e, a, a^2} and hence that G is isomorphic to the group.
(How do you get LaTeX to work here?)
There are currently 1 users browsing this thread. (0 members and 1 guests)
Bookmarks