LF\ - ORTHOaomi   OTERATDKS J!L
qrouviol the *u's x, = xa/ x3«0fej the ahflle. Jl ,* such a iPaq f tfak   Cf(1tofo) has all three.
tbuib   /V?   standard coordinihes
$>Q) ~ Ax .
Solution : (?)   Hfe W(i\ ff&t ikirutth* ($>X* in a &u(la\>\<L orthotooirvna6    ^£lS  an^f iher\
Where  s is the &ta*d**0l teste te*~($)<e*
jfests The firch vector (s irhe q&hew,U><r
0$ eh-—.-—,
)
Other two Vector   are   per fend<o»\ to it
1 * >o(<*>ot z*o 1
^//c direction
(D
Heh ce
%   % 0
% -% o
0    0 4
i s orthogonal toain'yt si'nce
' 1 vir? o
0    0 4
-1
l 12-    '2. Ol
(£) Anoiheir  £oln£fph   uea-s -bUe fach th&t
■b\\e Co In Mus   of*   the imttn'Y A A<s1t A^nAe^  .   So   v/e coi*p«i*z.
(D
SELFfiiddôlNT     Q?ERA WRS
L&t M and V be spaces wľéh Sazkír product over        öir (P.   Leb   cf> .< he « Iľ^atr
čf*  : V —y Ij ts  called   ad foittt  6>o <f / í f   foir aJl a eCi
aru?/ v e V
Wbeire 4 is 4 m^vx   k+*> .   Then cp*-/*  the »*/>/.,Wg <jr*čl)~4rffl
<W<8> =<*M,> -(4*)^ . ,r^Y
£yitopl& 2.    Had!*  V*^ (fOŕi^Av,
ecu {nation .     The  frcof- /i ŕŕrfl to the one aIpovb .
®
Theôtew Let oc be a* orthohoirynac fa^'s in 14f   A 4>» eríkohotmat kkisc*   ,}j ]/ ^.
anM   q>* : y-?tí. They)
T
£o\r íasIA awt ve V we q&t
čfirollah^    To ever^ Iihe4\r m4f>f>ľiu^ y : 14—y ]/ there is  a* 4#'joint   mapping ý>*
Let M be a vector space wůh * a&k* product Ah Ppeplbor (f : lj-*7t4 is calleof celfatfönb if fiov all <A,v&l/l
mtriH- Then    <f = is a eel-f&tjot'nL úpeměof-
to&bn'H.   Heíi   (f -   <C*-—><£"■ f q>Cf \ - A)' Hernu'tian  wiabriy      A - ( 2    c \
\ Zt^ 3-4r -y
pro^&cbľovi    onéo ůh<? £ctbspaos V £.1/1 The. (p (s d cclfoct joint  ope tuber . /.ere- 14 = Hi tn^)   v = f-/*^ ^i.^čr]/
a nd M2/ v* ér kx . n»<?«
E^fqein mines 4h#f <sity<?Mec£er£ o£ eelf^joth-b £>bemators
fs   Tea.1   (even if  \#e work over 4?j
(£)  EifrsHvector bo 4ifLfL*wt efyenwfre-* are pswy&d^ul^'r &ack -bo anobh<?ir.
Vrooj.  0   Le-t     q>Cu) - fa,    «*c? Then which   ^(V«s   ^ = >vf 4wi sv % fs real
4* Hir^O7- Theft
(V^J) <6^,
©
»*e> tests   o^K^,-,"*)   fame* b„ et'ie» recto* .  ,„ hh(& ^
Mere ^ ^rč?   d?^*W#es .
( 77>/i /3     * m lotete, to sťnľto.*  chlorem foir Uhťl&ir^ opem ůors
vtbho^owtt   probation  Oh  (mutual^ wbko^
where.    %- ate ^^etenb '*fé&#/ucs opO
& projection on k<?r
bteis   ť h   ÍR3   fernen by eiqeu vectors   of éh<z
A - 2  ž \
\2    2  Ý /
fflUCPCnOH    TO   QUŘĎŠQTIC FOJZVß
^ /H/
formed   ^íiř^^^ e>ľ$ek vec bote of
írfee (Ppe^a^o^ (f   ( of the yiatrt* A).    //* í^/Js b*s<s £<ie   vnetbri*   of  the čfUGútmkľc*
j^orvn    \S>   qiireto the  corresponding sykne.
©
So in -the CooräiViA^es of- the ortbohonnaO basis    <*    we k^e
Ä  *fflf2+ M* M*
iVf    which    é h er ^u^ämérľc f-&M>\ f: B?3^^1
has   d äiqo^t form,
HOH&wo&^iO      IZi'nd 4" er ukojena £ teste touch  hkc quzdwbc fom f :
/n
has   4 ^k'afoh^e  form.   ( ffiViér;        *r #e