digonal theorey
TRANSCRIPT
8/14/2019 digonal theorey
http://slidepdf.com/reader/full/digonal-theorey 1/26
Olmobpaduov abi Olmobpofyh~vYgo olmobpaduo z~hndoc lv a z~hndoc h` fhbvlio~ando
ygoh~oylfad lbyo~ovy abi }lio#~abmlbm azzdlfaylhb" @h~ owaczdo$ yglv z~hndoc lv f~uflad
lb vhdplbm v|vyocv h` il``o~obylad oquaylhbv$ abad|{lbm zhzudaylhb m~h}yg chiodv$ abi
fadfudaylbm zh}o~v h` cay~lfov 'lb h~io~ yh io`lbo ygo owzhbobylad cay~lw," Hygo~ a~oavvufg av zg|vlfv$ vhflhdhm|$ nlhdhm|$ ofhbhclfv abi vyaylvylfv gapo `hfuvoi
fhbvlio~ando ayyobylhb hb .olmobpaduov. abi .olmobpofyh~v.#ygol~ azzdlfaylhbv abi
ygol~ fhczuyaylhbv" No`h~o }o mlpo ygo `h~cad io`lblylhb$ doy uv lby~hiufo ygovo
fhbfozyv hb ab owaczdo"
Owaczdo" Fhbvlio~ ygo cay~lw
Fhbvlio~ ygo yg~oo fhducb cay~lfov
]o gapo
Lb hygo~ }h~iv$ }o gapo
Bowy fhbvlio~ ygo cay~lw Z `h~ }glfg ygo fhducbv a~o F 1$ F >$ abi F 6$ l"o"$
8/14/2019 digonal theorey
http://slidepdf.com/reader/full/digonal-theorey 2/26
]o gapo ioy ' Z , 3 79" Vh yglv cay~lw lv lbpo~ylndo" Oav| fadfudaylhbv mlpo
Bowy }o opaduayo ygo cay~lw Z #1 AZ " ]o doapo ygo ioyaldv yh ygo ~oaio~ yh fgofe ygay }o
gapo
Lb hygo~ }h~iv$ }o gapo
_vlbm ygo cay~lw cudylzdlfaylhb$ }o hnyalb
}glfg lczdlov ygay A lv vlclda~ yh a ilamhbad cay~lw" Lb za~ylfuda~$ }o gapo
`h~ Bhyo ygay ly lv adchvy lczhvvlndo yh `lbi A=? il~ofyd| `~hc ygo h~lmlbad
`h~c h` A"
Yglv owaczdo lv vh ~lfg h` fhbdfuvlhbv ygay cab| quovylhbv lczhvo ygocvodpov lb a
bayu~ad }a|" @h~ owaczdo$ mlpob a vqua~o cay~lw A$ gh} ih }o `lbi fhducb cay~lfov
}glfg gapo vlclda~ nogaplh~v av ygo anhpo hbov8 Lb hygo~ }h~iv$ gh} ih }o `lbi ygovo
fhducb cay~lfov }glfg }ldd godz `lbi ygo lbpo~ylndo cay~lw Z vufg ygay Z #1 AZ lv a
ilamhbad cay~lw8
8/14/2019 digonal theorey
http://slidepdf.com/reader/full/digonal-theorey 3/26
@~hc bh} hb$ }o }ldd fadd fhducb cay~lfov pofyh~v" Vh ygo anhpo fhducb cay~lfov
F 1$ F >$ abi F 6 a~o bh} pofyh~v" ]o gapo ygo `hddh}lbm io`lblylhb"
Io`lblylhb" Doy A no a vqua~o cay~lw" A bhb#{o~h pofyh~ F lv faddoi ab olmobpofyh~ h`
A l` abi hbd| l` ygo~o owlvyv a bucno~ '~oad h~ fhczdow, vufg ygay
L` vufg a bucno~ owlvyv$ ly lv faddoi ab olmobpaduo h` A" Ygo pofyh~ F lv faddoi
olmobpofyh~ avvhflayoi yh ygo olmobpaduo "
^oca~e" Ygo olmobpofyh~ F cuvy no bhb#{o~h vlbfo }o gapo
`h~ ab| bucno~ "
Owaczdo" Fhbvlio~ ygo cay~lw
]o gapo voob ygay
}go~o
Vh F 1 lv ab olmobpofyh~ h` A avvhflayoi yh ygo olmobpaduo :" F > lv ab olmobpofyh~ h` A
avvhflayoi yh ygo olmobpaduo #9 }gldo F 6 lv ab olmobpofyh~ h` A avvhflayoi yh ygo
olmobpaduo 6"
Ly ca| no lbyo~ovylbm yh ebh} }goygo~ }o `hubi add ygo olmobpaduov h` A lb ygo anhpo
owaczdo" Lb ygo bowy zamo$ }o }ldd ilvfuvv yglv quovylhb av }odd av gh} yh `lbi ygo
olmobpaduov h` a vqua~o cay~lw"
8/14/2019 digonal theorey
http://slidepdf.com/reader/full/digonal-theorey 4/26
@h~ a vqua~o cay~lw A h` h~io~ b$ ygo bucno~ lv ab olmobpaduo l` abi hbd| l` ygo~o
owlvyv a bhb#{o~h pofyh~ F vufg ygay
_vlbm ygo cay~lw cudylzdlfaylhb z~hzo~ylov$ }o hnyalb
Yglv lv a dlboa~ v|vyoc `h~ }glfg ygo cay~lw fho``lfloby lv " ]o advh ebh}
ygay yglv v|vyoc gav hbo vhduylhb l` abi hbd| l` ygo cay~lw fho``lfloby lv lbpo~ylndo$ l"o"
" Vlbfo ygo {o~h#pofyh~ lv a vhduylhb abi F lv bhy ygo {o~h
pofyh~$ ygob }o cuvy gapo
Owaczdo" Fhbvlio~ ygo cay~lw
Ygo oquaylhb y~abvdayov lbyh
}glfg lv oqulpadoby yh ygo quai~aylf oquaylhb
Vhdplbm yglv oquaylhb doaiv yh
8/14/2019 digonal theorey
http://slidepdf.com/reader/full/digonal-theorey 5/26
Lb hygo~ }h~iv$ ygo cay~lw A gav hbd| y}h olmobpaduov"
Lb mobo~ad$ `h~ a vqua~o cay~lw A h` h~io~ b$ ygo oquaylhb
}ldd mlpo ygo olmobpaduov h` A" Yglv oquaylhb lv faddoi ygo fga~afyo~lvylf oquaylhb h~
fga~afyo~lvylf zhd|bhclad h` A" Ly lv a zhd|bhclad `ubfylhb lb h` iom~oo b" Vh }o
ebh} ygay yglv oquaylhb }ldd bhy gapo ch~o ygab b ~hhyv h~ vhduylhbv" Vh a vqua~o
cay~lw A h` h~io~ b }ldd bhy gapo ch~o ygab b olmobpaduov"
Owaczdo" Fhbvlio~ ygo ilamhbad cay~lw
Lyv fga~afyo~lvylf zhd|bhclad lv
Vh ygo olmobpaduov h` I a~o a$ n$ f$ abi i $ l"o" ygo oby~lov hb ygo ilamhbad"
8/14/2019 digonal theorey
http://slidepdf.com/reader/full/digonal-theorey 6/26
Yglv ~ovudy lv padli `h~ ab| ilamhbad cay~lw h` ab| vl{o" Vh iozobilbm hb ygo paduov
|hu gapo hb ygo ilamhbad$ |hu ca| gapo hbo olmobpaduo$ y}h olmobpaduov$ h~ ch~o"
Ab|yglbm lv zhvvlndo"
^oca~e" Ly lv qulyo aca{lbm yh voo ygay ab| vqua~o cay~lw A gav ygo vaco olmobpaduov
av lyv y~abvzhvo AY nofauvo
@h~ ab| vqua~o cay~lw h` h~io~ >$ A$ }go~o
ygo fga~afyo~lvylf zhd|bhclad lv mlpob n| ygo oquaylhb
Ygo bucno~ 'a%i , lv faddoi ygo y~afo h` A 'iobhyoi y~ ' A,,$ abi fdoa~d| ygo bucno~
'ai #nf, lv ygo ioyo~clbaby h` A" Vh ygo fga~afyo~lvylf zhd|bhclad h` A fab no ~o}~lyyob
av
Doy uv opaduayo ygo cay~lw
N 3 A> # y~ ' A, A % ioy ' A, L >"
]o gapo
8/14/2019 digonal theorey
http://slidepdf.com/reader/full/digonal-theorey 7/26
]o doapo ygo ioyaldv yh ygo ~oaio~ yh fgofe ygay
Lb hygo~ }h~i$ }o gapo
Yglv oquaylhb lv ebh}b av ygo Fa|do|#Gacldyhb ygoh~oc" Ly lv y~uo `h~ ab| vqua~o
cay~lw A h` ab| h~io~$ l"o"
}go~o lv ygo fga~afyo~lvylf zhd|bhclad h` A"
]o gapo vhco z~hzo~ylov h` ygo olmobpaduov h` a cay~lw"
Ygoh~oc" Doy A no a vqua~o cay~lw h` h~io~ b" L` lv ab olmobpaduo h` A$ ygob;
1"
lv ab olmobpaduo h` Ac$ `h~
>"
L` A lv lbpo~ylndo$ ygob lv ab olmobpaduo h` A#1"
8/14/2019 digonal theorey
http://slidepdf.com/reader/full/digonal-theorey 8/26
8/14/2019 digonal theorey
http://slidepdf.com/reader/full/digonal-theorey 9/26
@l~vy }o dhhe `h~ ygo olmobpaduov h` A" Ygovo a~o mlpob n| ygo fga~afyo~lvylf oquaylhb
$ l"o"
L` }o iopodhz yglv ioyo~clbaby uvlbm ygo ygl~i fhducb$ }o hnyalb
_vlbm oav| admon~alf cablzudaylhbv$ }o moy
}glfg lczdlov ygay ygo olmobpaduov h` A a~o :$ #9$ abi 6"
Bowy }o dhhe `h~ ygo olmobpofyh~v"
1"
Favo ; Ygo avvhflayoi olmobpofyh~v a~o mlpob n| ygo dlboa~ v|vyoc
}glfg ca| no ~o}~lyyob n|
Cab| }a|v ca| no uvoi yh vhdpo yglv v|vyoc" Ygo ygl~i oquaylhb lv liobylfad yh
ygo `l~vy" Vlbfo$ `~hc ygo vofhbi oquaylhbv$ }o gapo | 3 0 w$ ygo `l~vy oquaylhb
8/14/2019 digonal theorey
http://slidepdf.com/reader/full/digonal-theorey 10/26
~oiufov yh 16 w % { 3 :" Vh yglv v|vyoc lv oqulpadoby yh
Vh ygo ubebh}b pofyh~ W lv mlpob n|
Ygo~o`h~o$ ab| olmobpofyh~ W h` A avvhflayoi yh ygo olmobpaduo : lv mlpob n|
}go~o f lv ab a~nly~a~| bucno~"
>"
Favo ; Ygo avvhflayoi olmobpofyh~v a~o mlpob n| ygo dlboa~ v|vyoc
}glfg ca| no ~o}~lyyob n|
Lb yglv favo$ }o }ldd uvo odocobya~| hzo~aylhbv yh vhdpo ly" @l~vy }o fhbvlio~
ygo aumcobyoi cay~lw $ l"o"
8/14/2019 digonal theorey
http://slidepdf.com/reader/full/digonal-theorey 11/26
Ygob }o uvo odocobya~| ~h} hzo~aylhbv yh ~oiufo ly yh a uzzo~#y~labmuda~
`h~c" @l~vy }o lbyo~fgabmo ygo `l~vy ~h} }lyg ygo `l~vy hbo yh moy
Bowy$ }o uvo ygo `l~vy ~h} yh odoclbayo ygo ? abi 0 hb ygo `l~vy fhducb" ]o
hnyalb
L` }o fabfod ygo 7 abi < `~hc ygo vofhbi abi ygl~i ~h}$ }o hnyalb
@lbadd|$ }o vuny~afy ygo vofhbi ~h} `~hc ygo ygl~i yh moy
Bowy$ }o voy { 3 f" @~hc ygo vofhbi ~h}$ }o moy | 3 > { 3 >f" Ygo `l~vy ~h} }ldd
lczd| w 3 #> |%6 { 3 #f" Gobfo
8/14/2019 digonal theorey
http://slidepdf.com/reader/full/digonal-theorey 12/26
Ygo~o`h~o$ ab| olmobpofyh~ W h` A avvhflayoi yh ygo olmobpaduo #9 lv mlpob n|
}go~o f lv ab a~nly~a~| bucno~"
>"
Favo ; Ygo ioyaldv `h~ yglv favo }ldd no do`y yh ygo ~oaio~" _vlbm vlclda~
lioav av ygo hbo iovf~lnoi anhpo$ hbo ca| oavld| vgh} ygay ab| olmobpofyh~ W
h` A avvhflayoi yh ygo olmobpaduo 6 lv mlpob n|
}go~o f lv ab a~nly~a~| bucno~"
^oca~e" Lb mobo~ad$ ygo olmobpaduov h` a cay~lw a~o bhy add ilvylbfy `~hc oafg hygo~
'voo ygo zamo hb ygo olmobpaduov `h~ ch~o ioyaldv," Lb ygo bowy y}h owaczdov$ }o
ilvfuvv yglv z~hndoc"
Owaczdo" Fhbvlio~ ygo cay~lw
8/14/2019 digonal theorey
http://slidepdf.com/reader/full/digonal-theorey 13/26
8/14/2019 digonal theorey
http://slidepdf.com/reader/full/digonal-theorey 14/26
Lb hygo~ }h~iv$ ab| olmobpofyh~ W h` A avvhflayoi yh ygo olmobpaduo #1 lv a dlboa~
fhcnlbaylhb h` ygo y}h olmobpofyh~v
Owaczdo" Fhbvlio~ ygo cay~lw
Ygo fga~afyo~lvylf oquaylhb lv mlpob n|
Gobfo ygo cay~lw A gav hbo olmobpaduo$ l"o" #6" Doy uv `lbi ygo avvhflayoi
olmobpofyh~v" Ygovo a~o mlpob n| ygo dlboa~ v|vyoc
}glfg ca| no ~o}~lyyob n|
8/14/2019 digonal theorey
http://slidepdf.com/reader/full/digonal-theorey 15/26
Yglv v|vyoc lv oqulpadoby yh ygo hbo oquaylhb#v|vyoc
w# |
3 :"
Vh l` }o voy w 3 f$ ygob ab| olmobpofyh~ W h` A avvhflayoi yh ygo olmobpaduo #6 lv mlpob
n|
Doy uv vucca~l{o }gay }o ili lb ygo anhpo owaczdov"
Vucca~|; Doy A no a vqua~o cay~lw" Avvuco lv ab olmobpaduo h` A" Lb h~io~ yh `lbi
ygo avvhflayoi olmobpofyh~v$ }o ih ygo `hddh}lbm vyozv;
1"
]~lyo ih}b ygo avvhflayoi dlboa~ v|vyoc
>"
Vhdpo ygo v|vyoc"
6"
^o}~lyo ygo ubebh}b pofyh~ W av a dlboa~ fhcnlbaylhb h` ebh}b pofyh~v"
Ygo anhpo owaczdov avvuco ygay ygo olmobpaduo lv ~oad bucno~" Vh hbo ca| }hbio~
}goygo~ ab| olmobpaduo lv ad}a|v ~oad" Lb mobo~ad$ yglv lv bhy ygo favo owfozy `h~
v|ccoy~lf cay~lfov" Ygo z~hh` h` yglv lv po~| fhczdlfayoi" @h~ vqua~o cay~lfov h`
8/14/2019 digonal theorey
http://slidepdf.com/reader/full/digonal-theorey 16/26
h~io~ >$ ygo z~hh` lv qulyo oav|" Doy uv mlpo ly go~o `h~ ygo vaeo h` nolbm dlyydo fhczdoyo"
Fhbvlio~ ygo v|ccoy~lf vqua~o cay~lw
Lyv fga~afyo~lvylf oquaylhb lv mlpob n|
Yglv lv a quai~aylf oquaylhb" Ygo bayu~o h` lyv ~hhyv '}glfg a~o ygo olmobpaduov h` A,
iozobiv hb ygo vlmb h` ygo iovf~lclbaby
_vlbm admon~alf cablzudaylhbv$ }o moy
Ygo~o`h~o$ lv a zhvlylpo bucno~ }glfg lczdlov ygay ygo olmobpaduov h` A a~o ~oad
bucno~v"
^oca~e" Bhyo ygay ygo cay~lw A }ldd gapo hbo olmobpaduo$ l"o" hbo ihundo ~hhy$ l` abi
hbd| l` " Nuy yglv lv zhvvlndo hbd| l` a3f abi n3:" Lb hygo~ }h~iv$ }o gapo
A 3 a L >"
Lb ygo bowy zamo$ }o }ldd ilvfuvv ygo favo h` fhczdow olmobpaduov"
@l~vy doy uv fhbplbfo hu~vodpov ygay ygo~o owlvy cay~lfov }lyg fhczdow olmobpaduov"
Owaczdo" Fhbvlio~ ygo cay~lw
8/14/2019 digonal theorey
http://slidepdf.com/reader/full/digonal-theorey 17/26
Ygo fga~afyo~lvylf oquaylhb lv mlpob n|
Yglv quai~aylf oquaylhb gav fhczow ~hhyv mlpob n|
Ygo~o`h~o ygo cay~lw A gav hbd| fhczdow olmobpaduov"
Ygo y~lfe lv yh y~oay ygo fhczdow olmobpaduo av a ~oad hbo" Coablbm }o ioad }lyg ly av a
bucno~ abi ih ygo bh~cad fadfudaylhbv `h~ ygo olmobpofyh~v" Doy uv voo gh} ly }h~ev
hb ygo anhpo owaczdo"
]o }ldd ih ygo fadfudaylhbv `h~ " Ygo avvhflayoi olmobpofyh~v a~o mlpob
n| ygo dlboa~ v|vyoc
A W 3 '1%>l, W
}glfg ca| no ~o}~lyyob av
8/14/2019 digonal theorey
http://slidepdf.com/reader/full/digonal-theorey 18/26
Lb `afy ygo y}h oquaylhbv a~o liobylfad vlbfo '>%>l,'>#>l, 3 7" Vh ygo v|vyoc ~oiufov yh
hbo oquaylhb
'1#l, w
# |
3 :"
Voy w3f$ ygob | 3 '1#l,f" Ygo~o`h~o$ }o gapo
}go~o f lv ab a~nly~a~| bucno~"
^oca~e" Ly lv fdoa~ ygay hbo vghudi owzofy yh gapo fhczdow oby~lov lb ygo
olmobpofyh~v"
]o gapo voob ygay '1#>l, lv advh ab olmobpaduo h` ygo anhpo cay~lw" Vlbfo ygo oby~lov h`
ygo cay~lw A a~o ~oad$ ygob hbo ca| oavld| vgh} ygay l` lv a fhczdow olmobpaduo$
ygob lyv fhbkumayo lv advh ab olmobpaduo" Ch~ohpo~$ l` W lv ab olmobpofyh~ h` A
avvhflayoi yh $ ygob ygo pofyh~ $ hnyalboi `~hc W n| yaelbm ygo fhczdow#fhbkumayo h` ygo oby~lov h` W $ lv ab olmobpofyh~ avvhflayoi yh " Vh ygo olmobpofyh~v
h` ygo anhpo cay~lw A avvhflayoi yh ygo olmobpaduo '1#>l, a~o mlpob n|
}go~o f lv ab a~nly~a~| bucno~"
Doy uv vucca~l{o }gay }o ili lb ygo anhpo owaczdo"
8/14/2019 digonal theorey
http://slidepdf.com/reader/full/digonal-theorey 19/26
Vucca~|; Doy A no a vqua~o cay~lw" Avvuco lv a fhczdow olmobpaduo h` A" Lb
h~io~ yh `lbi ygo avvhflayoi olmobpofyh~v$ }o ih ygo `hddh}lbm vyozv;
1"
]~lyo ih}b ygo avvhflayoi dlboa~ v|vyoc
>"
Vhdpo ygo v|vyoc" Ygo oby~lov h` W }ldd no fhczdow bucno~v"
6"
^o}~lyo ygo ubebh}b pofyh~ W av a dlboa~ fhcnlbaylhb h` ebh}b pofyh~v }lyg
fhczdow oby~lov"
9"
L` A gav ~oad oby~lov$ ygob ygo fhbkumayo lv advh ab olmobpaduo" Ygo avvhflayoi
olmobpofyh~v a~o mlpob n| ygo vaco oquaylhb `hubi lb 6$ owfozy ygay }o vghudi
yaeo ygo fhbkumayo h` ygo oby~lov h` ygo pofyh~v lbphdpoi lb ygo dlboa~
fhcnlbaylhb"
Lb mobo~ad$ ly lv bh~cad yh owzofy ygay a vqua~o cay~lw }lyg ~oad oby~lov ca| vyldd gapo
fhczdow olmobpaduov" Hbo ca| }hbio~ l` ygo~o owlvyv a fdavv h` cay~lfov }lyg hbd|
~oda olmobpaduov" Yglv lv ygo favo `h~ v|ccoy~lf cay~lfov" Ygo z~hh` lv po~| yofgblfad
abi }ldd no ilvfuvvoi lb abhygo~ zamo" Nuy `h~ vqua~o cay~lfov h` h~io~ >$ ygo z~hh` lv
qulyo oav|" Doy uv mlpo ly go~o `h~ ygo vaeo h` nolbm dlyydo fhczdoyo"
Fhbvlio~ ygo v|ccoy~lf vqua~o cay~lw
8/14/2019 digonal theorey
http://slidepdf.com/reader/full/digonal-theorey 20/26
8/14/2019 digonal theorey
http://slidepdf.com/reader/full/digonal-theorey 21/26
Avvuco ygo~o owlvyv a ilamhbad cay~lw I vufg ygay A 3 Z #1 IZ " Ygob }o gapo
l"o lv vlclda~ yh " Vh ygo| gapo ygo vaco fga~afyo~lvylf oquaylhb"
Gobfo A abi I gapo ygo vaco olmobpaduov" Vlbfo ygo olmobpaduov h` I h` ygo bucno~v
hb ygo ilamhbad$ abi ygo hbd| olmobpaduo h` A lv >$ ygob }o cuvy gapo
Lb yglv favo$ }o cuvy gapo A 3 Z #1 IZ 3 > L >$ }glfg lv bhy ygo favo" Ygo~o`h~o$ A lv bhy
vlclda~ yh a ilamhbad cay~lw"
Io`lblylhb" A cay~lw lv ilamhbadl{ando l` ly lv vlclda~ yh a ilamhbad cay~lw"
^oca~e" Lb a z~oplhuv zamo$ }o gapo voob ygay ygo cay~lw
gav yg~oo il``o~oby olmobpaduov" ]o advh vgh}oi ygay A lv ilamhbadl{ando" Lb `afy$ ygo~o
lv a mobo~ad ~ovudy adhbm ygovo dlbov"
Ygoh~oc" Doy A no a vqua~o cay~lw h` h~io~ b" Avvuco ygay A gav b ilvylbfy
olmobpaduov" Ygob A lv ilamhbadl{ando" Ch~ohpo~$ l` Z lv ygo cay~lw }lyg ygo fhducbv
F 1$ F >$ """$ abi F b ygo b olmobpofyh~v h` A$ ygob ygo cay~lw Z #1 AZ lv a ilamhbad cay~lw"
Lb hygo~ }h~iv$ ygo cay~lw A lv ilamhbadl{ando"
Z~hndoc; ]gay gazzoboi yh vqua~o cay~lfov h` h~io~ b }lyg dovv ygab b olmobpaduov8
]o gapo a za~ylad abv}o~ yh yglv z~hndoc"
8/14/2019 digonal theorey
http://slidepdf.com/reader/full/digonal-theorey 22/26
Ygoh~oc" Doy A no a vqua~o cay~lw h` h~io~ b" Lb h~io~ yh `lbi huy }goygo~ A lv
ilamhbadl{ando$ }o ih ygo `hddh}lbm vyozv;
1"
]~lyo ih}b ygo fga~afyo~lvylf zhd|bhclad
>"
@afyh~l{o " Lb yglv vyoz$ }o vghudi no ando yh moy
}go~o ygo $ $ ca| no ~oad h~ fhczdow" @h~ opo~| l$ ygo
zh}o~v bl lv faddoi ygo 'admon~alf, cudylzdlfly| h` ygo olmobpaduo "
6" @h~ opo~| olmobpaduo$ `lbi ygo avvhflayoi olmobpofyh~v" @h~ owaczdo$ `h~ ygo
olmobpaduo $ ygo olmobpofyh~v a~o mlpob n| ygo dlboa~ v|vyoc
Ygob vhdpo ly" ]o vghudi `lbi ygo ubebh}b pofyh~ W av a dlboa~ fhcnlbaylhb h` pofyh~v$ l"o"
}go~o $ a~o a~nly~a~| bucno~v" Ygo lbyomo~ cl lv faddoi ygo
mohcoy~lf cudylzdlfly| h` "
8/14/2019 digonal theorey
http://slidepdf.com/reader/full/digonal-theorey 23/26
9"
L` `h~ opo~| olmobpaduo ygo admon~alf cudylzdlfly| lv oquad yh ygo mohcoy~lf
cudylzdlfly|$ ygob }o gapo
}glfg lczdlov ygay l` }o zuy ygo olmobpofyh~v F k$ }o hnyalboi lb 6" `h~ add ygo
olmobpaduov$ }o moy owafyd| b pofyh~v" Voy Z yh no ygo vqua~o cay~lw h` h~io~ b
`h~ }glfg ygo fhducb pofyh~v a~o ygo olmobpofyh~v F k" Ygob Z lv lbpo~ylndo abi
lv a ilamhbad cay~lw }lyg ilamhbad oby~lov oquad yh ygo olmobpaduov h` A" Ygo
zhvlylhb h` ygo pofyh~v F k lb Z lv liobylfad yh ygo zhvlylhb h` ygo avvhflayoi
olmobpaduo hb ygo ilamhbad h` I" Yglv liobyly| lczdlov ygay A lv vlclda~ yh I"
Ygo~o`h~o$ A lv ilamhbadl{ando"
^oca~e" L` ygo admon~alf cudylzdlfly| bl h` ygo olmobpaduo lv oquad yh 1$
ygob hnplhuvd| }o gapo cl 3 1" Lb hygo~ }h~iv$ bl 3 cl"
?"
L` `h~ vhco olmobpaduo ygo admon~alf cudylzdlfly| lv bhy oquad yh ygo mohcoy~lf
cudylzdlfly|$ ygob A lv bhy ilamhbadl{ando"
Owaczdo" Fhbvlio~ ygo cay~lw
Lb h~io~ yh `lbi huy }goygo~ A lv ilamhbadl{ando$ dy uv `hddh} ygo vyozv iovf~lnoi
anhpo"
1"
Ygo zhd|bhclad fga~afyo~lvylf h` A lv
8/14/2019 digonal theorey
http://slidepdf.com/reader/full/digonal-theorey 24/26
Vh #1 lv ab olmobpaduo }lyg cudylzdlfly| > abi #> }lyg cudylzdlfly| 1"
>"
Lb h~io~ yh `lbi huy }goygo~ A lv ilamhbadl{ando$ }o hbd| fhbfoby~ayo u~
ayyobylhb hb ygo olmobpaduo #1" Lbiooi$ ygo olmobpofyh~v avvhflayoi yh #1$ a~o
mlpob n| ygo v|vyoc
Yglv v|vyoc ~oiufov yh ygo oquaylhb # | % { 3 :" Voy abi $ ygob
}o gapo
Vh ygo mohcoy~lf cudylzdlfly| h` #1 lv > ygo vaco av lyv admon~alf cudylzlfly|"
Ygo~o`h~o$ ygo cay~lw A lv ilamhbadl{ando" Lb h~io~ yh `lbi ygo cay~lw Z }o
booi yh `lbi ab olmobpofyh~ avvhflayoi yh #>" Ygo avvhflayoi v|vyoc lv
}glfg ~oiufov yh ygo v|vyoc
8/14/2019 digonal theorey
http://slidepdf.com/reader/full/digonal-theorey 25/26
Voy $ ygob }o gapo
Voy
Ygob
Nuy l` }o voy
ygob
8/14/2019 digonal theorey
http://slidepdf.com/reader/full/digonal-theorey 26/26
]o gapo voob ygay l` A abi N a~o vlclda~$ ygob Ab fab no owz~ovvoi oavld| lb yo~cv h`
Nb" Lbiooi$ l` }o gapo A 3 Z #1 NZ $ ygob }o gapo Ab 3 Z #1 Nb Z " Lb za~ylfuda~$ l` I lv a
ilamhbad cay~lw$ Ib lv oav| yh opaduayo" Yglv lv hbo azzdlfaylhb h` ygo ilamhbadl{aylhb"
Lb `afy$ ygo anhpo z~hfoiu~o ca| no uvoi yh `lbi ygo vqua~o ~hhy abi funlf ~hhy h` a
cay~lw" Lbiooi$ fhbvlio~ ygo cay~lw anhpo
Voy
ygob
Gobfo A 3 Z I Z #1" Voy
Ygob }o gapo
N6 3 A"
Lb hygo~ }h~iv$ N lv a funlf ~hhy h` A"