<p>Let T be an operator on an n-dimensional vector space V and let A = [T]
be its matrix in the ordered basis b = {x1,…,xn}. Let B = (P^-1)AP, where
P = [pij ] is an invertible n x n matrix. Is B the matrix of T in some ordered
basis for V ? Prove your answer.</p>
<p>Omit… <_<</p>
<p>@TCBH</p>
<p>That one should pop out nicely if you can find a way to P as a change of basis matrix. Which I think you can do because P is invertible and therefore the vectors (p1ix1), (p2ix2) … (pnixn) are linearly independent and thus would form another basis of V.</p>
<p>B would then be the matrix representation of T under the “new” basis. Therefore B is similar to A</p>
<p>B=(P^-1)AP</p>
<p>Math gives me hives. <em>cringe</em></p>
<p>What Keynesian economics is… :)</p>
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<p>I don’t think that fact about invertible matrices is (explicitly) in the course notes, which complicates matters. Of course invertible => null space = {0} => one to one => linear independent sets –> linear independent sets => basis –> new basis => P is a change of basis matrix => B = [T] in the new basis</p>
<p>Though I used a much more complicated method, as did the TA oddly enough.</p>
<p>
A system or idea to stimulate the supply of money to get our economy out of a deficit/depression/recession by raising reserves, lowering interest rates and buying government bonds. Coined by John Maynard Keynes.</p>
<p>@ Millancad, why do they hate me? </p>
<p>Because I do everything better than them.
Spelling was easy as well, vocabulary I loved. I read encyclopedias and stuff on astrophysics in like 3rd grade.</p>
<p>^um, you read stuff on astrophysics in third grade?</p>
<p>Pigs have orgasms for 30 minutes at a time.</p>
<p>^^^ Haha wait until you actually go to MIT, the asians there pwn everyone!!</p>
<p>^lol :).</p>
<p>lol there, I will meet a challenge. I think I might be the top african american in my school, if not the county or region academically.</p>
<p>Yes I read stuff on astrophysics. It’s amazing what parents make a child do.</p>
<p>0.o why was everyone reading intense encyclopedias during elementary school? The only trivia I remember reading was like the Guinness Book of World Records or Ripley’s Believe it or not.</p>
<p>But I eventually moved out of the factual stage and started reading a lot of chick lit. </p>
<p>And astrophysics during 3rd grade?! Erm, what a childhood. I think I did mathy puzzle things for fun, but that’s about it.</p>
<p>And to address the OP, I don’t think it’s really necessary to use an esoteric vocabulary to impress. More often than not, you come off as pretentious, which isn’t really an admirable trait.</p>
<p>“I think I might be the top african american in my school, if not the county or region academically.”</p>
<p>Dear MIThopeful, you need to get out more :). Wait until you get to college - I don’t doubt you’re above-this-world amazing, but you’ll definitely meet people in your life who’ll blow you away in some way.</p>
<p>Oh, psychology. </p>
<p>People just BS some crud on psychology a lot, facts they randomly heard. Overall I’ve never met anyone about to study psychology who didn’t come off as a total pretentious snob.</p>
<p>True Convo:
mathguy- haha yeah
Psychgirl- hmmm…<em>rolls eyes</em>
mathguy- …you think you’re smarter than me don’t you?
Psychgirl- no…I know I am</p>
<p>But she honestly hadn’t done anything to prove she’s smarter than him besides use a kinda big vocabulary. And talk about once studying in french, but really, nothing much. She was just…a real *****. I never understood people like that, there’s one guy like that at school about math because he always figures he’s right. But really I prove him wrong a lot but he never admits it “oh, that’s what I was kinda meant!” or “yeah, but my way also get’s there!” and it’s just no. That wasn’t what you meant or where you were going. He’ll just never admit he’s wrong.</p>
<p>I think a way to honestly appear smarter is to ask for help and admit when wrong. Otherwise you’ll come off as a ******.</p>
<p>I just read and quote authors every once in a while, and last year I had this Plato obsessed teacher so I’ve quoted Plato a few times too…
This seems to make me “seem smarter” to other people but usually I try not to act all superior and smart though. I really don’t feel I am, I haven’t read enough older works.
And who cares if people think you aren’t really smart and knowledgeable, your achievements will make you stand out when it really matters.</p>
<p>Erm, actually in my experience math guys are the pretentious snobs. (atleast some of them). Or perhaps a more apt term would be *******s.</p>
<p>I hate psychology. Math is cool.</p>
<p>hahahaha, this is hilarious, i genuinely love it :]</p>