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MATH2601 Higher Linear Algebra (1 Viewer)

InteGrand

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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
I don't know if this was the reason why, but in the Q you typed above, there's a typo (top-right entry should have 6 rather than 5 in the square root).
 

leehuan

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I don't know if this was the reason why, but in the Q you typed above, there's a typo (top-right entry should have 6 rather than 5 in the square root).
Oops. Nah I think that was just a typo as I typed it on the forums
 

leehuan

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This one's a bit long...





Proven in i): 0 is the only eigenvalue of B (so B is nilpotent)



 

leehuan

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Oh of course. Once I drew out the Jordan chain again and looked carefully at what the question gave iii made sense.
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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
 
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leehuan

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No more questions for this sem after tomorrow.
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leehuan

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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?
 

InteGrand

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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:










I did not even know that there was a sum form until doing past papers for 1251. Then I had to figure out why the sum and vector forms were equivalent.
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/Octogon/volumes/volume1/article1_19.pdf .
 

leehuan

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Completely forgot about that one.
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leehuan

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This is just some personal fun

 
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turtlesnore

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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?)
 

InteGrand

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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?)
What was your progress on the questions so far?

Also to use LaTeX on the forums here, you need to enclose TeX code in so-called "tex tags". (Using LaTeX here is a bit different to just using it on your own computer.) You need to enclose the TeX code in between: [tex.] [/tex.] (but leave out the red dots).

For example: typing

[tex.] y = x^{2}[/tex.]

(but deleting the red dots) gives

.
 

turtlesnore

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I thought about using the identity and inverse axioms but I couldn't get anywhere with them. I thought that it would be straight forward that since there are only 3 elements in G, so either or . But I was confused when I saw that part b said because that wouldn't be consistent with my result, and implies that doesn't necessarily have to be written in G to be in the set G.

Thanks for the LaTeX help.
 

InteGrand

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I thought about using the identity and inverse axioms but I couldn't get anywhere with them. I thought that it would be straight forward that since there are only 3 elements in G, so either or . But I was confused when I saw that part b said because that wouldn't be consistent with my result, and implies that doesn't necessarily have to be written in G to be in the set G.

Thanks for the LaTeX help.


 

marxman

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By the same token, how do we prove in the first place?
 

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