Re: [obm-l] Complexos e Matrizes

[niski <fabio@xxxxxxxxx>]

>>E para complexos ? Ha alguma demonstracao GEOMETRICA de quei i^2 = -1 ?
> 
> 
> Aqui eu não tenho a menor idéia do que é que você espera: i^2 = -1
> é o fato mais básico sobre i, não sei em que contexto faria sentido
> demonstrar (geometricamente ou de qualquer outra forma) que i^2 = -1.

Professor Nicolau talvez algo possa ser tirado dos quaternions do 
Hamilton (não me aprofundei muito mas quaternions = vetores?) Veja um 
pedaço da carta de Sir W. R. Hamilton ao seu filho Archibald.

"But on the 16th day of the same month - which happened to be a Monday, 
and a Council day of the Royal Irish Academy - I was walking in to 
attend and preside, and your mother was walking with me, along the Royal 
Canal, to which she had perhaps driven; and although she talked with me 
now and then, yet an under-current of thought was going on in my mind, 
which gave at last a result, whereof it is not too much to say that I 
felt at once the importance. An electric circuit seemed to close; and a 
spark flashed forth, the herald (as I foresaw, immediately) of many long 
years to come of definitely directed thought and work, by myself if 
spared, and at all events on the part of others, if I should even be 
allowed to live long enough distinctly to communicate the discovery. Nor 
could I resist the impulse - unphilosophical as it may have been - to 
cut with a knife on a stone of Brougham Bridge, as we passed it, the 
fundamental formula with the symbols, i, j, k; namely,

     i^2 = j^2 = k^2 = ijk = -1 "

Hamilton se explica melhor em uma carta ao matematico John T. Graves, a 
carta pode ser vista em pdf: 
http://www.maths.tcd.ie/pub/HistMath/People/Hamilton/QLetter/QLetter.pdf
ou html
http://www.maths.tcd.ie/pub/HistMath/People/Hamilton/QLetter/QLetter.html

Acho que disso pode-se tirar algumas informacoes e relacoes entre 
vetores numeros complexos e geometria, ou estou enganado?

Um abraço.
-- 
Niski - http://www.linux.ime.usp.br/~niski

"When we ask advice, we are usually looking for an accomplice."
Joseph Louis LaGrange

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