[線代] canonical quotient map
我想證的是3 而且是從R is onto--->T is onto
我的證法是
如果R是onto 那代表每個z都可以找到v+W s.t. R(v+W)=z
既然可以找到v+W 代表一定能找到一個v在V裡 s.t q(v)=v+W
但是我不知道是否可以這樣證
如果不行 想請教一下板友要怎麼證
謝謝
LetV and Z be vectors paces over a field F, let W be a subspace of V, and let
q:V àV/W be the canonical quotient map. Let T : V -à Z be a linear map such
that W is contained in ker(T ). Prove the following:
1. There exists a unique linear map R : V/W à Z such that T = Roq (i.e.
composition). (Hint: The equation T = Roq tells you how to define R. Check
that this definition is ‘well-defined’ and gives a linear map with the
desired property. Then show any other linear map with this property must be
R.)
3. The map R from part(1)is onto if and only if T is onto.
--
※ 發信站: 批踢踢實業坊(ptt.cc)
◆ From: 128.97.245.124
推
02/17 19:28, , 1F
02/17 19:28, 1F
→
02/17 19:56, , 2F
02/17 19:56, 2F