tranformaciones de lorentz

8/17/2019 Tranformaciones de Lorentz

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UNIVERSIDAD NACIONAL DEL SANTA

«Una Universidad joven Formando líderes

para el desarrollo de la Región y el País»

DATOS PERSONALES

TEMA:

TRANSFORMACIONES DE LORENTZ


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AUTORES:

GOMEZ MELENDEZ GULLYTPONTE GOICOCHEA SCHNEIDERRODRIGUEZ JACINTO ALEXANDER

VEGA AQUIÑO JHON


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CURSO:

FÍSICA IV

ESCUELA:


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Ingenier! en Energ!


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C"i#$%&e ' Per()*+,

TRANSFORMACIONES DE LORENTZ

L!- &r!n-.%r#!/i%ne- 0e L%ren&12 0en&r% 0e 3! &e%r! 0e 3! re3!&i4i0!0e-5e/i!32 -%n 6n /%n76n&% 0e re3!/i%ne- 86e 0!n /6en&! 0e /9#% -ere3!/i%n!n 3!- #e0i0!- 0e 6n! #!gni&60 .-i/! %$&eni0!- 5%r 0%-%$-er4!0%re- 0i.eren&e-: E-&!- re3!/i%ne- e-&!$3e/ier%n 3! $!-e #!&e#;&i/!


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0e 3! &e%r! 0e 3! re3!&i4i0!0 e-5e/i!3 0e Ein-&ein2

En e3 !>% +?*@2 Ein-&ein2 56$3i/9 3! &e%r! 0e 3! Re3!&i4i0!0 E-5e/i!3 %Re-&ringi0!2 $!-!0! en 3%- 0%- 5%-&63!0%- .6n0!#en&!3e- -ig6ien&e-


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+: Todas las leyes físicas son las mismas o sea! "e#manecenin$a#ian%es& "a#a %odos los o'se#$ado#es ine#ciales es%o es! conmo$imien%o #ela%i$o de %#aslaci(n )nifo#me&* E-&e 5%-&63!0% eB&ien0e e35rin/i5i% 0e 3! Re3!&i4i0!0 0e G!3i3e% 0e 3! Me/;ni/! ! &%0!- 3!- 3e


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neg!&i4% 0e3 eB5eri#en&% 0e Mi/"e3-%n < M%r3e


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5!r! &%0%- 3%- %$-er4!0%re- iner/i!3e-: !7% e-&!- -65%-i/i%ne-2 3!&r!n-.%r#!/i9n 0e G!3i3e% n% e- 4;3i0!2 en 5!r&i/63!r 3! e/6!/i9n & & n%56e0e -er /%rre/&!: Si 3! 4e3%/i0!0 0e 3! 361 e- 3! #i-#! 5!r! 0%-%$-er4!0%re- /%n #%4i#ien&% re3!&i4% 6ni.%r#e2 n% e- 5%-i$3e2 /%#% -e 4er;0e-56-2 86e 3%- 0%- #i0!n e3 #i-#% &ie#5%: En %&r!- 5!3!$r!-2 e3 in&er4!3%0e &ie#5% en&re 0%- e4en&%- n% &iene 5%r 86 -er e3 #i-#% 5!r!

%$-er4!0%re- en #%4i#ien&% re3!&i4%: En 0e.ini&i4! 0e$e#%- ree#53!1!r 3!&r!n-.%r#!/i9n G!3i3e!n! 5%r %&r!2 0e #%0% 86e 3! 4e3%/i0!0 0e 3! 361 -e!in4!ri!n&e:


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C%n.%r#e n%- 4!#%- .!#i3i!ri1!n0% #;- < #;- /%n 3!- /%n-e/6en/i!- 0e3%- 5%-&63!0%- 0e Ein-&ein2 -e 46e34e 0e-e!$3e %$&ener .9r#63!- 0e /!r;/&er gener!3 86e n%- 5er#i&!n %$&ener &%0! 3! in.%r#!/i9n 86e 0e-/ri$! 3%-e4en&%- !n!3i1!0%- 5%r 0%- %$-er4!0%re- en #%4i#ien&% re3!&i4% e3 6n% /%nre-5e/&% !3 %&r%2 0%- %$-er4!0%re- -i&6!0%- en 0%- #!r/%- 0e re.eren/i!0i-&in&%- S < S -e !/%-&6#$r! 0en%&!r !3 %$-er4!0%r en re5%-% /%#% 6n

%$-er4!0%r /%3%/!0% en e3 #!r/% 0e re.eren/i! S #ien&r!- 86e e3 %$-er4!0%r #94i3 0e-53!1;n0%-e ! 6n! 4e3%/i0!0 V e-&; 56e-&% en e3 #!r/% 0ere.eren/i! 0e-ign!0% /%#% S


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T!3e- e/6!/i%ne- 0e &r!n-.%r#!/i9n 0e /!r;/&er gener!3 0e 6n #!r/% 0ere.eren/i! ! %&r% .6er%n en6n/i!0!- 5%r 4e1 5ri#er! n% 5%r Ein-&ein -in% 5%r e3 .-i/% L%ren&12 r!19n 5%r 3! /6!3 re/i$en e3 n%#$re 0e e/6!/i%ne- 0e&r!n-.%r#!/i9n 0e L%ren&1:

P!r! 3! 0eri4!/i9n 0e 3!- e/6!/i%ne- 0e &r!n-.%r#!/i9n2 en !#$%- #!r/%-

0e re.eren/i! -e /en&r!r; 3! !&en/i9n -%$re 6n e4en&% /%#(n 0e-/ri&% 5%r !#$!- 5er-%n!-2 e3 /6!3 &en0r; /%%r0en!0!- B2


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P%r -i#53i/i0!0 en 3! 0eri4!/i9n 0e 3!- e/6!/i%ne- 0e &r!n-.%r#!/i9n2 !#$%-#!r/%- 0e re.eren/i! -%n -e3e//i%n!0%- 0e #%0% &!3 86e -6- %rgene- e356n&% O en e3 #!r/% 0e re.eren/i! 0e S < e3 56n&% O en e3 #!r/% 0ere.eren/i! 0e S /%in/i0!n en 3%- &ie#5%- &* < &*:

S659ng!-e 86e /6!n0% 3%- %rgene- 0e !#$%- #!r/%- 0e re.eren/i!

/%in/i0en -e 0i-5!r! 6n 563-% 0e 361 en e3 %rigen /%#(n 0e !#$%-: P%r e3-eg6n0% 5%-&63!0% 0e 3! Te%r! E-5e/i!3 0e 3! Re3!&i4i0!02 e-&e 563-% 0e 361-e 5r%5!g!r; /%n 3! #i-#! 4e3%/i0!0 &!n&% 0en&r% 0e3 #!r/% 0e re.eren/i! S/%#% 0en&r% 0e3 #!r/% 0e re.eren/i! S: E-&e e- 5re/i-!#en&e e3 56n&% /3!4e5!r! 5%0er %$&ener 3! &r!n-.%r#!/i9n 0e 6n #!r/% 0e re.eren/i! ! %&r%2 e3


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"e/"% 0e 86e 3! 4e3%/i0!0 0e 3! 361 / 86e 0e$e -er 3! #i-#! en !#$%-#!r/%- 0e re.eren/i!2 &!n&% 5!r! e3 #!r/% 0e re.eren/i! S

/ B K &

B /&

C%#% 5!r! e3 #!r/% 0e re.eren/i! S

/ B K &


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B /&

C6;3 e- e3 &i5% 0e &r!n-.%r#!/i9n 86e e-&!#%- $6-/!n0% Si re/%r0!#%- 3!0eri4!/i9n 0e 3%- re-63&!0%- 5re3i#in!re- -%$re 3%- .en9#en%- 0e 3!0i3!&!/i9n 0e3 &ie#5% < 3! /%n&r!//i9n 0e 3%ngi&602 re-63&! /3!r% 86e 3!-&r!n-.%r#!/i%ne- 86e e-&!#%- $6-/!n0% 0e$en -er &r!n-.%r#!/i%ne-

3ine!re-: E-&!n0% .i7! 3! 4e3%/i0!0 V ! 3! /6!3 -e 0e-53!1! e3 #!r/% 0ere.eren/i! S2 -i 5%r 3! 0i3!&!/i9n 0e3 &ie#5% #e0i0% en S /6!n0% -e #i0e enS re86iere 0e 3! !53i/!/i9n 0e 6n .!/&%r 0e /%rre//i9n /%n-&!n&e e-&% e-2 -i3! 4e3%/i0!0 V e- &!3 86e /6!n0% 6n 3!5-% 0e &ie#5% #e0i0% en S e- 0e +*-eg6n0%- en&%n/e- e3 3!5-% 0e &ie#5% #e0i0% en S e- 0e +@ -eg6n0%-2 /%n


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3% /6!3 !3 #!n&ener-e /%n-&!n&e e3 .!/&%r 0e /%rre//i9n en&%n/e- 6n 3!5-% 0e&ie#5% 0e )* -eg6n0%- #e0i0% en S e86i4!30r; ! 6n 3!5-% 0e &ie#5% 0e *-eg6n0%- #e0i0% en S 0e3 #i-#% #%0% 86e 6n 3!5-% 0e &ie#5% 0e *-eg6n0%- #e0i0% en S e86i4!30r; ! 6n 3!5-% 0e &ie#5% 0e ,@ -eg6n0%-#e0i0% en S e3 .!/&%r 0e /%rre//i9n 0e$e -er 6n! -i#53e /%n-&!n&e#63&i53i/!&i4! /6


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0e3 &ie#5%: Y en 3% 86e /%n/ierne ! 3! /%n&r!//i9n 0e 3%ngi&602 &!#$in !33 !30e-/6$rir e3 .en9#en% 0e 3! /%n&r!//i9n 0e 3%ngi&60 en/%n&r!#%- 86e e3.!/&%r 0e /%rre//i9n re86eri0% er! 6n! /%n-&!n&e #63&i53i/!&i4!: En !#$%-/!-%-2 ne/e-i&!#%- 0e &r!n-.%r#!/i%ne- 3ine!re-: Si 3!- &r!n-.%r#!/i%ne- n%.6e-en 3ine!re-2 6n! 3%ngi&60 B)=B+ #e0i0! en e3 #!r/% 0e re.eren/i! S0e5en0er! 0e 3! -e3e//i9n 0e3 %rigen 0e3 #!r/% 0e re.eren/i!2 < 6n in&er4!3%

0e &ie#5% &)=&+ 0e5en0er! 0e /6;n0% e3 &ie#5% .6e -e3e//i%n!0% 5!r! &ener 6n 4!3%r 0e /er% en /ier&! .%r#! 3! n%=3ine!3i0!0 n%- 33e4!r! 0e regre-%"!/i! 3%- /%n/e5&%- 0e3 &ie#5% !$-%36&% < 3! 0i-&!n/i! !$-%36&!: P%r %&r%3!0%2 56e-&% 86e e3 #%4i#ien&% re3!&i4% en&re !#$%- #!r/%- 0e re.eren/i! S


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< S %/6rre (ni/!#en&e en 3! 0ire//i9n 0e 3%- e7e- 0e 3!- e86i- B2 3!-/%%r0en!0!- y < + 0e$en 5er#!ne/er ig6!3e-2 % -e! y y < + +-:

C6!n0% %/6rre e3 e4en&% en e3 /6!3 e3 563-% 36#in%-% 0i-5!r!0% /6!n0% 3%-%rgene- O < O 0e !#$%- #!r/%- 0e re.eren/i! /%in/i0!n 33eg! !3 56n&% P20e !/6er0% /%n 3! 5er-5e/&i4! 0e3 %$-er4!0%r en S e3 #!r/% 0e re.eren/i!

#94i3 S -e "! 0e-53!1!0% "!/i! 3! 0ere/"! 6n! 0i-&!n/i! 0e V& en 6n &ie#5%& #e0i0% 5%r e3 %$-er4!0%r en S: Per% &!#$in 0e-0e 3! 5er-5e/&i4! 0e3%$-er4!0%r en S2 6n! 4!r! 0e #e0ir 33e4!0! /%n-ig% 5%r S ! 3% 3!rg% 0e3 e7e0e 3!- e86i- B -e "! /%n&r!0% 5%r 6n .!/&%r 0e /%rre//i9n /%n-&!n&e 86e


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33!#!re#%- !: P!r! e3 %$-er4!0%r .i7%2 5%r 3% &!n&%2 3! re3!/i9n en&re -6 #!r/%0e re.eren/i! < e3 #!r/% 0e re.eren/i! #94i3 0e$e -er

B !B $&

B !B $K! &

En 0%n0e ! < $ -%n -i#53e- /%n-&!n&e- #63&i53i/!&i4!- .!/&%re- 3ine!re- 86e-%n in0e5en0ien&e- 0e B < &:


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A- /%#% 3%- .en9#en%- 0e 3! re3!&i4i0!0 -e 46e34en /!0! 4e1 #;-e4i0en&e- ! 4e3%/i0!0e- /er/!n!- ! 3! 4e3%/i0!0 0e 3! 3612 !3g% 86e &!#$in0e$e -er /ier&% e- 86e ! $!7!- 4e3%/i0!0e- 3!- e/6!/i%ne- 0e &r!n-.%r#!/i9n86e "e#%- e-/ri&% !rri$! -e 0e$en re06/ir ! 3%- re-63&!0%- /3;-i/%- 86e

B B = V&

En %&r!- 5!3!$r!-2 5!r! 4!3%re- $!7%- 0e VK/2 ! 0e$e !/er/!r-e ! + < $K!0e$e !/er/!r-e ! V2 3! &r!n-.%r#!/i9n re3!&i4i-&! -e 0e$e re06/ir ! 3!


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&r!n-.%r#!/i9n /3;-i/! 5!r! $!7!- 4e3%/i0!0e- 0e V: E-&% n%- 5er#i&ee-/ri$ir 3! &r!n-.%r#!/i9n re3!&i4i-&! /%#%

B !B V&

L! &r!n-.%r#!/i9n in4er-! 0e$e &ener 3! #i-#! .%r#!2 eB/e5&% 5%r e3 /!#$i%

0e -ign% in4%36/r!0% 5%r e3 "e/"% 0e 86e e3 #!r/% 0e re.eren/i! S -e e-&;0e-53!1!n0% "!/i! 3! i186ier0! #ien&r!- 86e e3 #!r/% 0e re.eren/i! S5er#!ne/e e-&;&i/%:

B !B = V&


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Per%


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/& ! /& V&

/& ! / V &


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/& ! / = V +K/ ! / V &

/ & ! / = V &

De 3% /6!3 %$&ene#%- 5!r! ! 3% -ig6ien&e

! / K / = V

! + K + = VK/


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! + K + = VK/

! : C%n e-&%

B B V&

P%0e#%- %$&ener 3! e/6!/i9n 0e &r!n-.%r#!/i9n 5!r! e3 &ie#5% 0e 3!e/6!/i9n

B !B = V&


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6-!n0%

B !B V&

5!r! &

B ! ! B V& = V&

0e 3% /6!3

& !& ! = +K! BKV


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& ! & VB K/

Re-6#ien0%2 < e#53e!n0% e3 -#$%3% en 36g!r 0e !2 5!r! /!#$i!r 0e3#!r/% 0e re.eren/i! S 86e -e e-&; #%4ien0% 0e i186ier0! ! 0ere/"! ! 6n!4e3%/i0!0 V !3 #!r/% 0e re.eren/i! S 0e3 %$-er4!0%r e-&!/i%n!ri%2 3!-

e/6!/i%ne- 0e &r!n-.%r#!/i9n 0e L%ren&1 -%n

B B V&

<


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1 1

& & VBK/

P%0e#%- %$&ener 3! &r!n-.%r#!/i9n in4er-! 5!r! /!#$i!r 0e3 #!r/% 0e

re.eren/i! S !3 #!r/% 0e re.eren/i! S 0ire/&!#en&e 0e 3!- !n&eri%re-e/6!/i%ne-: De 3! 5ri#er! e/6!/i9n < 0e 3! /6!r&! e/6!/i9n2 5%0e#%-ree-/ri$ir3!- en .%r#! &!3 86e &!n&% 3! 4!ri!$3e B /%#% 3! 4!ri!$3e & 56e0!n-er 0e-5e7!0!- 5%r #e0i% 0e e/6!/i%ne- -i#63&;ne!- 5%r #e0i% 0e


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0e&er#in!n&e- !53i/!n0% 3! reg3! 0e Cr!#er % /6!386ier %&r! &/ni/!#!&e#;&i/! 0e3 g6-&% 0e3 e-&60i!n&e

B V& BK

VK/ B & &K


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E- !- /%#% %$&ene#%- e3 -ig6ien&e /%n76n&% 0e e/6!/i%ne-

B B = V&


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O$-r4e-e 86e2 eB/e5&6!n0% 5%r 3! 0i.eren/i! en&re 3%- -ign%- W < W= en&re3! 5ri#er! < 3! /6!r&! e/6!/i9n 0e !#$!- &r!n-.%r#!/i%ne-2 !#$!-&r!n-.%r#!/i%ne- -%n /%#53e&!#en&e -i#&ri/!-: L! 0i.eren/i! en e3 -ign%-i#53e#en&e in0i/! 86e #ien&r!- 86e 5!r! e3 %$-er4!0%r en S 3! 5er-%n! enS -e e-&; #%4ien0% en 6n! 0ire//i9n 5%-i&i4! "!/i! 3! 0ere/"!2 5!r! 3!5er-%n! en S e3 %$-er4!0%r en S -e e-&; #%4ien0% en -en&i0% /%n&r!ri%2 en

6n! 0ire//i9n neg!&i4! "!/i! 3! i186ier0!:

En 4ir&60 0e 86e -e re86iere !3g% 0e 5r;/&i/! 5!r! 5%0er !086irir /ier&!0e-&re1! en e3 e#53e% 0e 3!- &r!n-.%r#!/i%ne- 0e L%ren&1 5!r! 3! re-%36/i9n0e 5r%$3e#!-2 ! /%n&in6!/i9n 4ere#%- !3g6n%- e7er/i/i%- 86e n%- 0!r;n 6n!


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.!#i3i!ri0!0 en 3! &r!n-.%r#!/i9n 0e /%%r0en!0!- 0e 6n -i-&e#! 0ere.eren/i! ! %&r%: Se %$-er4!r; 86e e-&!- &r!n-.%r#!/i%ne- 0e /%%r0en!0!-n% -%n #6< 0i.eren&e- ! 3!- &r!n-.%r#!/i%ne- /3;-i/!- 0e /%%r0en!0!- 0eG!3i3e%2 eB/e5&% 86e 3!- .9r#63!- 86e e#53e!#%- !86 -e $!-!n en 3!4!3i0e1 0e 3%- 0%- 5%-&63!0%- 0e 3! Te%r! E-5e/i!3 0e 3! Re3!&i4i0!0:


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PRO.LEMA: P!r! 6n %$-er4!0%r O 6n 0e-&e33% 0e 361 -!3e 0e3 56n&% B +** i39#e&r%-2 < )* i39#e&r%-2 1 * i39#e&r%- en 6n &ie#5% & *:***@-eg6n0%: C6;3e- -%n 3!- /%%r0en!0!- 0e3 e4en&% 5!r! 6n -eg6n0%%$-er4!0%r O 86e -e #6e4e /%n re-5e/&% !3 5ri#er% ! 3% 3!rg% 0e3 e7e /%#(n

B=B ! 6n! 4e3%/i0!0 0e V =*:/

E3 .!/&%r 0e /%rre//i9n en e-&e /!-% e-

+ K + = VK/ + K + = =*: + K *:[ +:[[\


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De 3!- &r!n-.%r#!/i%ne- 0e L%ren&1 5!r! 5!-!r 0e3 -i-&e#! 0e re.eren/i! S!3 -i-&e#! 0e re.eren/i! S &ene#%- en&%n/e- 3% -ig6ien&e

B B = V& +:[[\+** ]# = =*: ^+* #K-eg @^+*=, -eg [\ ]#


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De e-&! #!ner!2 e3 e4en&% &iene 3!- -ig6ien&e- /%%r0en!0!-

En S B2


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0i.eren/i! en&re 3!- /%%r0en!0!- 0e 0%- e4en&%- 0i-&in&%- < /%#5!r!r 0i/"!0i.eren/i! 0e 6n #!r/% ! %&r%:

PRO.LEMA: Deri4!r2 e#53e!n0% 3!- &r!n-.%r#!/i%ne- 0e L%ren&12 3!.9r#63! 5!r! 3! 0i3!&!/i9n 0e3 &ie#5%2 e-5e/i.i/!n0% 3!- /%%r0en!0!- 0e /!0!e4en&% in4%36/r!0% en e3 !n;3i-i-:

E- -6.i/ien&e /%n-i0er!r (ni/!#en&e 0%- e4en&%- 5!r! 3! re-%36/i9n 0e e-&e5r%$3e#!: E3 5ri#er e4en&% e- !863 en e3 /6!3 3%- re3%7e- 0e S < S e-&;n e36n% .ren&e !3 %&r%2 -in/r%ni1!0%-


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E3 -eg6n0% e4en&% e- !863 en e3 /6!32 0e !/6er0% /%n e3 %$-er4!0%r en e3

-i-&e#! S2 e3 re3%7 en S -e "! #%4i0% 0e 6n! 5%-i/i9n B+ ! 6n! 5%-i/i9n B)en -6 e7e 0e /%%r0en!0!-


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O$-r4e-e 86e 86e 5!r! e3 re3%7 4i!7er% 3! /%%r0en!0! 5%-i/i9n B 0en&r% 0e-6 #!r/% 0e re.eren/i! S n% /!#$i! en 3% !$-%36&%2


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Se! _& &) = &+ e3 in&er4!3% 0e &ie#5% 5r%5i% #e0i0% 0en&r% 0e3 #!r/% 0ere.eren/i! S en 6n #i-#% 56n&% .i7% B* 0en&r% 0e3 #!r/% 0e re.eren/i! S: E3in&er4!3% 0e &ie#5% _& en&re 3%- 0%- e4en&%- 86e /%rre-5%n0e !3 #!r/% 0ere.eren/i! S 56e0e -er %$&eni0% 0e 3!- e/6!/i%ne- 0e &r!n-.%r#!/i9n 0eL%ren&1

&) &) V B)K/ &) V B*K/

&+ &+ V B+K/ &+ V B*K/

_& &) = &+


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_& &) V B*K/ = &+ V B*K/

_& &) = &+

_& _&

E-&e e- e3 .en9#en% re3!&i4i-&! 0e 3! 0i3!&!/i9n 0e3 &ie#5%: He#%- %$&eni0%0ire/&!#en&e ! 5!r&ir 0e 3!- &r!n-.%r#!/i%ne- 0e L%ren&1 3! re3!/i9n 5!r! 3!0i3!&!/i9n 0e3 &ie#5% 0e 6n re3%7: L! re-%36/i9n 0e3 5r%$3e#! re86iri90e&er#in!r 3%- e4en&%- -%$re 3%- /6!3e- -e 33e4!r! ! /!$% 3! &r!n-.%r#!/i9n


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0e 3!- /%%r0en!0!-: Un! 4e1 86e -e "!n 3%gr!0% 0e&er#in!r 3%- e4en&%-2 e35r%$3e#! e-&; 5r;/&i/!#en&e re-6e3&%:

PRO.LEMA: Deri4!r2 e#53e!n0% 3!- &r!n-.%r#!/i%ne- 0e L%ren&12 3!.9r#63! 5!r! 3! /%n&r!//i9n 0e 3%ngi&60:


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C%n-i0re-e 6n! 4!r! 0e #e0i/i9n /6


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U-!n0% 3!- re3!/i%ne- 0e &r!n-.%r#!/i9n 0e L%ren&12 &ene#%- 3% -ig6ien&e

B) B) = V&) B) = V&*

B+ B+ = V&+ B+ = V&*

P%r 3% &!n&%

B) = B+ B) = V&* = B+ = V&*

B) = B+ B) = B+


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B) = B+ B) = B+ K

L L*K

E & 3 . 9 3 &i i & 0 3 & i9 0 3 i& 0

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