K Gc 7¥31 - University of California,...
1
Coordinatizing 2/26/2019 → → Choosing a basis B = Ebb , bn } ← Isomorphism B :lRdimV- V - , T : VFW bijective 4 he x. bit - . - txnbi E.ge ① 1B = { axkbxtclasb.cc IR } B = { K2 , K , 13 B : 1123 → Pa via [ I ] It ax 't bxtc , x4xt2 word a ]B=[ I ] ② V= Col [ If ] = { ( § ] I a. BER } 13={11%1,193} B : R' → V via Cab ] It all ]tb[ 7) = [ § ] Deth CoordinatesofvEVwlrHB# : 043=1%41 stv-x.be - - t Kati ( i.e B- ' Cv ) in the map B 112dm V above ) Matrix of a linear map - T : V → W linear Let BIC be a basis of VIN . IT ]B is a matrix such that the V , have IT ]BHB = ( Tbc Fact IT ] , = 4Th ]c - [ Tbn ] ) E.g T : Bz → Pa , pox , ↳ ( Gc - Dpw ) ' K ' t 3×2 - 2x Take B=C= Ex ; x , 13 K IT 2x - I ° o 7 1-7 y IT IB = 7¥31 o , " ) Check TCx4xt2 ) = ( CKD Gated ) ' = ( 23+2-2 ) ' [1%4111]=1 ? ] ← 3¥ , = 30041
Transcript of K Gc 7¥31 - University of California,...
Coordinatizing 2/26/2019
→ →
Choosing a basis B = Ebb . .
,bn } ← Isomorphism B :lRdimV- V
- ,
T : VFW bijective 4he x. bit - . - txnbi
E.ge ① 1B = { axkbxtclasb.cc IR }.
B = { K2,
K, 13
.
B : 1123 → Pa via [ I ] It ax 't bxtc,
x4xt2 word.
a ]B=[ I ]② V= Col [ If ] = { ( § ] I a. BER }
.
13={11%1,193}B : R' → V via Cab ] It all ]tb[ 7) = [ § ]
Deth CoordinatesofvEVwlrHB# :
043=1%41stv-x.be- - - t Kati
.( i.e. B- ' Cv ) in the
map B -
-112dm V above )
Matrix of a linearmap-
T : V → W linear.
Let BICbe a basis of VIN.
IT]Bis a matrix such that the V,
have
IT]BHB = (Tbc.
Fact IT ],
=
4Th]c - - - [Tbn])E.g T : Bz → Pa
, pox , ↳ (
Gc- Dpw )
'K
'
t 3×2 - 2x
Take B=C= Ex ; x, 13
.
K IT 2x - I
° o7 1-7 yITIB = 7¥31o
,
"
) . Check TCx4xt2 ) = ( CKD Gated )'
= ( 23+2-2 )'
[1%4111]=1 ?] ← 3¥ ,.
= 30041
