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Comments:
<0> no
<1> 2t+1=A*(t+1)+B, sorry
<2> how would one go about finding from A=[4,-1,1,6;0,0,-3,3;4,1,0,14;4,1,3,2] Minor(1,3) and the Cofactor(1,3)
<0> Manny : yes that's better
<1> if I'd just read what I wrote on my paper, but I'm a bit tired :)
<3> peachfuzz - with the definition
<0> Manny : but it is clear now ?
<0> Manny : didn't you switch from EE to math last year ?
<1> _kmh_: no, I'm still doing EE :/
<0> oh i thought you had decided on switching ?
<0> so you stick to EE ?
<1> yup, they have quite interesting applications of differential equations :)
<0> hahaha
<0> ok
<1> let me think...factoring an i-th degree real null in the denominator, I can get I sum terms where each of the elements has a rational scalar in the numerator, and a null^k factor in the denominator.
<1> s^think^summarize^
<1> believe it or not, when you do decent circuit theory, you'll stumble across phase portraits, lots of linear algebra, differential equations etc. Also, I'm to interested in physics to just focus on maths :/.
<1> I'm getting more and more convinced that you shouldn't study maths unless you can give something to it, i.e. you're a genius and can contribute new solutions. If I were elegible for studying maths, I'd answer questions here instead of asking them :).
<4> that's like saying you should only become an artist if you're going to be the next da vinci, monet, or pic***o
<1> HiLander: hrm I think the problem with this analogy is that artists do arts because they want others to enjoy their works, and even works by myself could be enjoyed. But maths is really some sort of hard science, i.e. you focus methods and problem solutions that can be tought to others instead of focusing on some emotional momentum.
<5> HiLander: Correct. And I sometimes agree to that statement too.
<6> Manny: math is art also
<1> I for myself often enjoy other's elegant solutions, but I think I couldn't come up with such solutions. I'm sometimes struck by the difference of formal and informal perception. Informal doesn't care what's right or provable, but what's aesthetic, and often wrong things are very aesthetic.
<1> s^Informal^Informalism^
<0> Manny : you don't need only "contributors" in math, you staff and teachers as well
<0> Manny : and you should study if you like the material, after all to large degree you study for your personal benefit/enlightment rather than to contribute/better the world
<5> Good teaching is contribution too.
<0> yes
<0> but not in Manny's oroginal meaning
<0> i.e. contribution on the genius level or whatever
<1> _kmh_: right, and I'm very good at school maths because I think I've exactly the right balance between formalism and informalism for that, but I often need quite some time for understanding sophisticated proofs, which shows that I'll never be elegible for teaching on universities or such, because you have to know many aspects of a matter to teach it good.
<5> I am at the genius level in teaching.
<1> note that I don't confuse informalism and lack of comprehension, but I have enough of both, as some of my questions show :).
<1> thanks for your help! :)
<1> see you
<7> Hi
<7> I need some help finishing a proof about normal operators
<8> can't help with the proof, but maybe you should define 'normal'
<8> that's quite vague.
<7> The exercise statement is: if A, B are normal operators (matrices) that commute, then AB is normal
<7> normal as in AA*=A*A
<7> where A* is the hermitian adjoint
<9> so you need to show AB(AB)*=(AB)*AB
<7> exactly
<9> so, find (AB)* in terms of A*, B*
<7> I got a solution more or less worked out when the vectorial space over which the operator are defined has finite dimension
<9> hmm, i dont think dimension should matter here
<7> My proof so far is: A and B are normal => they are diagonalizable
<7> since they commute, they are simultaneously diagonalizable
<7> => their product similar to a diagonal matrix
<8> what section of mathematics is that problem from?
<7> Pete_I: linear algebra
<8> mpupu, thank you.
<7> maybe functional analysis, not sure
<7> well, I guess I'm on my own
<7> thanks anyways
<10> http://upload.wikimedia.org/math/6/5/3/653be1d7481f0247e9a9d1b12f5a8878.png , whats the third symbol called, before the upside down triangle ?
<7> qbert: gamma?
<10> thx
<10> whats the upside down triangle called :)
<7> it's a greek letter, don't know if it has a special meaning in there
<9> nabla?
<10> the one that looks like a y sort of ?
<11> qbert: ya, that's gamma
<10> ok thx
<11> the triangle is an upside down "Delta", but i dont know it's english name
<8> it's nabla.
<8> http://en.wikipedia.org/wiki/Nabla_symbol
<8> shows a picture in the first paragraph.
<9> hmm an inverted delta is a nabla, a gamma is like a gallows. but i hae los tt he battery for my mouse so canbt look at the link
<7> thief_grr: no, delta is the rightside-up triangle
<12> how is it a greek letter?
<7> Sturgeon: alpha, beta, gamma,...
<8> _llll_, don't have a backup mouse?
<9> no, justa battery-operated one
<7> actually, the real meaning for nabla there is this: http://en.wikipedia.org/wiki/Del
<10> wireless mice ****
<7> it's a differential operator
<9> am beginning to suspect someone has stolen the other battery
<10> pirates ?
<12> mpupu: and then nabla?
<8> ninjas?
<11> mpupu: i said up-side down ;)
<9> it is a possibilty
<7> thief_grr: you're right
<12> mpupu: it comes after which letter of the greek alpabet?
<11> mpupu: i'm greek :P
<7> Sturgeon: i meant gamma
<9> thief_grreek?
<11> _llll_: heheh, greeks think so, it's short for grrrrr though.
<11> any recommendations for introductory books on ODEs, preferably with no physics inside?
<12> Coddington & Levinson
<11> not on amazon :|
<12> it's old :\
<11> found one from just coddington, 1989
<11> maybe it's practically the same book
<12> http://www.amazon.com/gp/product/0070992568/104-1424182-2422362?v=glance&n=283155
<12> no, it's not
<11> Sturgeon: yeah i found that..
<11> not in stock from amazon ;)
<13> Sturgeon: There are 2 possibnle things u can say on a matrix, that its diagnoisable, aka exists A=P^-1DP , and its......
<13> Sturgeon: whats the english word for it?
<13> to make all zeroes below the diagon or above it
<14> Copter, triangular?
<13> yea probably
<14> upper-triangular or lower-triangular
<13> and how can u say if it can be turned into trianglar?
<13> Trianglarable? :P
<14> triangularizable
<13> thx
<14> What is your word for it?
<13> I know the term in hebrew :P
<14> Ah, that's not one of my languages. Wouldn't do me much good to know
<9> well you can always go to Jordan Normal form o(over C)
<13> _llll_: Yea was just wondering on the english word for it
<13> oh btw I went to improve the grade on algebra 2 today and failed :(
<13> I think most of the people that took this one failed.
<9> I've missed more than 9,000 shots in my career. I've lost almost 300
<9> games. 26 times I've been trusted to take the game winning shot and
<9> missed. I've failed over, and over and over again in my life. And
<9> that is why I succeed. --- Michael Jordan
<13> :o
<13> Is that real? :)
<9> dunno
<10> if w is a vector what does ||w|| mean ? the whole example is 'select a weight where w_o < ||w||'
<13> qbert: sqrt of <w,w> ? :o
<9> ||w|| is the norm of w
<9> ie some kind of "length"
<10> ahh thx
<10> hmm covariance means to very different things in math and programming :/
<14> and in tensor notation
<14> and in statistics
<10> way to make it confusing math community
<9> what does covariance mean in programming?
<10> when overriding a base cl*** function, the function is 'covariant' if it matches its base cl***es function signature
<10> http://msdn2.microsoft.com/en-us/library/ms173174.aspx
<10> better : http://www.answers.com/topic/covariance-and-contravariance
<14> It is probably related in some vague way to a covariance in category theory
<9> well category theory has used co and contravaraince since 1945
<9> tensor stuff will be older
<14> (or borrowed because of a misunderstanding)
<9> i dotn really see how the programming thing is related
<14> neither do I
<14> I'm trying to think of covariant functors.
<14> Tensor covariance is clearly irrelevant
<14> Oh well, just another overloaded term.
<9> so i'd blame the oprgrammers for misusing the term, but maybe there is some relation here
<14> A Haskell programmer might understand the connection
<15> hello
<15> is there any good reading material on the "butterfly effect" ?
<16> chaos by james gleick is a cl***ic if you want a whole book
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