A 7P£A/P/X
V'£'ClOR   SVPiCES.   WITH SCfiLAf> TR00I4CT
Ďe fínt hon     Let U he a tecboy ^paC<s dwr ^
billíneair fotm wŕth Corresponding ^a^lm tic   foirm   positive útefŕn('6c.l (\e. r& me*"*
(T)        <I4< V> a
(D        <ÍU/H>   >0    fioir CiíO*
^xanfúle 0   Siahdaircfi rc&fafr product oh
Etaw^e~-(D   C r^/^J ^ ^fe trecom S/aace £>f-
Defi'yttlt'on     Let 64 be a vector cjpa^e, over €  ( eefey. ttukubers.)     4 m#f>
<  ,    >   :   //* H -> &
is   Oallevt   4 sözk.^  product H
■ «
Were bat"   —   means cop^pley.
= 44~ 14.2.
Example (£)   g-b&uAwd scalar product
- 3 -
Space of- Continuous   Cotopte* fuhcbx'o^s 0Y\ the Cntemrzô Ľ4, .
The norm g?/ £Ae vec&or   (A & U ťs
£:X4t*tpJe.    fens/Weir IK*1 \fibh &k<*.n4/a.vt>ŕ zcal&r product. Then
Two vectors  utv e 14 are. ott^omt '"f <M^> = č?. '
Hte write    u ± v .
Let 14,1/ čri/l , Then
\<^(v>\ ±ll«IIHrll
The &?UQ.lľt<4 i's $«st for linea r/y aŕe/eetfo^ut vectors   u ana/ v.
-4-
l£yjwp/e. Consider IA- uyt'Gh sbwrtfy ZO&l&ir product. Then
lYoof-   f.Q\r   real   Q\paa* M If    v » O* then
tfKd'  theorem   holds. If-   v^o9( censiMeir 6he sectors for a/I t €r7R
0 ^ //fcf-tf //2 - ^tv-u, tv-ny =.
77//!s *s   fuadimtrib    pofyhotnfot ih & Vvhi'oVi  cs   ±o.   That is fjyhq its *t(kcn'~ toift&nh     D   is     le« or etfiidl to Ot
\<uiv>\ * MM . ^
r/?<f eofu^/ft^ occurs <py>/t(   cf ~0