~The Council Of Youngers of BYC! (COY)~

[Gerbil]

Oh my gosh it's Gerbil!
How'ya been buddy?

It may be indeed.

Buzzy, seriously. I am all collegiate and stuffs now. All sorts of hooplah and funs.

What about yourself?

 

[Gerbil]

Hello Adam. Hello Ooj. Wazzup, how are mah homiez? (lol, I can't believe I just typed that...)

Random facts you can [re]familiarise yourselves with if you wish... (or just ignore it because it's for my notes. I forgot my book.)



An nxn matrix has exactly n eigenvalues.

A matrix with an eigenvalue of 0 is not invertible.

An eigenspace is a subspace of dimension at most equal to the multiplicity of its corresponding eigenvalue.


Eigenvectors corresponding to distinct eigenvalues are linearly independent. Proof by induction.

True for one eigenvector: eigenvectors are not 0, so the equation cv = 0 has only the trivial solution and v is linearly independent. (What was the point of that...)

Assume it's true for k eigenvectors.

Now consider the set of eigenvectors up to v(k+1). To prove the set is linearly independent we show that all the constants in c(1)v(1) + .... +c(k)v(k) + c(k+1)v(k+1) = 0 are zero. (EQ 1)

Multiply this equation by A. Each term becomes c(k)A.v(k), which is also c(k)L(k)v(k) because eigenvectors are awesome like that. (EQ 2)

Multiply the original equation by L(k+1). (EQ 3)

EQ 2 - EQ 3 removes the final term involving v(k+1). This means we only have eigenvectors 1 through k left in the equation. Those are linearly independent so their coefficients must be 0. As none of the eigenvectors are the same, L(n)-L(k+1) can't ever be zero. That means all the constants have to be 0. If c(1) through c(k) are zero, EQ 1 is reduced to c(k+1)v(k+1) = 0. v(k+1) is not zero because it's an eigenvector.

Therefore c(k+1) is zero and the equation has only the trivial solution and the set is linearly independent.

*inserts induction conslusion sentence*




I've forgotten to bring my notebook to uni so I have to memorise key facts from the maths lecture to write down later. I scheduled this hour for watching the lecture recording and there's no way I'm doing it again.

I will keep this page loaded on my phone to write it up later. (much better than the other options, a) typing on my phone, b) depleting my printing quota and half a tree, c) having to move to go get my USB and then having to load that onto my ancient laptop again, which is always a battle to turn on, d) watching it again tomorrow. )

*Nods and smiles*

Not much here, lol.
Waz 'sup yourself (Aside from that brain-begoggling definition)?

 

[Fierlin1182]

BYC has so many uses.

That it does, lol.
I did get those notes written down last night, albeit in very sloppy handwriting because I'd had about three hours' sleep the night before, and as a consequence muscle co-ordination wasn't in top form yesterday.

Now it's time to tackle some integration by reduction formula questions.

...Maybe later.

Moin Adam, mir geht's gut. Seit lange habe ich kein Deutsch gesprochen. Aber vor kurzem habe ich einen neuen Fruend kennengelernt, der ein bisschen Deutsch spricht (weil er ein paar Jahren in Deutschland gewohnt hat). Wir arbeiten zusammen, aber heutzutage habe ich nichts intelligent auf Deutsch zu sagen, besonderes unter Druck am Samstagmorgen.

 

[Chickenrandomness]

It may be indeed.

Buzzy, seriously.

I am all collegiate and stuffs now. All sorts of hooplah and funs.

What about yourself?

Fun! XD

I am good! Got into the hobby of airsoft, been preparing for military stuff, and I only have 1 more year of school

 

[Fierlin1182]

OOJ! ES GIBT HIER JETZT EIN PARTY!!!

 

[Fierlin1182]

Die Leute sind alle wieder zusammen!


...Kind of

 

[Fierlin1182]

*Nods and smiles*

Not much here, lol.
Waz 'sup yourself (Aside from that brain-begoggling definition)?

Not much. My team came fourth in the Not So Amazing Race on Friday, just missing out on one of the very expensive-looking prize packages I helped to pack. Rats! If only we'd been bothered to get the people on the tram doing the YMCA, we could've gotten enough bonus points to scrape in...

Yeah, fun in the German club. I'm quite glad I joined the German club. ;P

 

[Gerbil]

Fun! XD

I am good! Got into the hobby of airsoft, been preparing for military stuff, and I only have 1 more year of school

Airsoft is cool! Most of the time. At least I think so. My brother is not totally sure, not after our last little game. Ehheeheehee.
Cool, cool. All mah peeples iz growin' up.

 

[Gerbil]

Not much. My team came fourth in the Not So Amazing Race on Friday, just missing out on one of the very expensive-looking prize packages I helped to pack. Rats! If only we'd been bothered to get the people on the tram doing the YMCA, we could've gotten enough bonus points to scrape in...

Yeah, fun in the German club. I'm quite glad I joined the German club. ;P

OOJ! ES GIBT HIER JETZT EIN PARTY!!!

ಠ_ಠ Ich bin der Party ...

Daaw, well, I guess better luck next time.
I've only participated in a couple runs. My team did win the last Ironman I was in though! We got medals. Cool medals. I feel like I should have more medals. Yes.

I think there is a German club on my campus to.. Wish I spoke some. lol, I only know like three words. All from watching Hogan's Heroes.

 

[Fierlin1182]

ಠ_ಠ Ich bin der Party ...

Daaw, well, I guess better luck next time.
I've only participated in a couple runs. My team did win the last Ironman I was in though! We got medals. Cool medals. I feel like I should have more medals. Yes.

I think there is a German club on my campus to.. Wish I spoke some. lol, I only know like three words. All from watching Hogan's Heroes.

lol, that ends up happening when one is watching foreign TV. I have been watching The Bridge, and I have learned two Swedish words. I'm not very impressed by my achievements.

Du bist der Arty in der Party. Kannst du das erinnern?

I thought we deserved at least one packet of nerds. There were so many nerds split between 1st, 2nd and 3rd prize.
I did get to do a chicken dance around a random stranger on the street though (which was one of the bonus challenges) so it was all good.