Chapter 3 3 3.1 Mathematic review 1.Vector Space (or Linear Space )if it satisfies with 1)Sums "1+1=1+ for all&in V (:+;)=(+:)+T;for allv,vin V 1+(-)=(-）+1:0 1,-I inV 1+0:01:1 re V 2)Products (a)1(r:）=(n n1,"2 are real numbers,V (b)r ()=r+r:isareal number,:e V (c)(2)=+1,rare real numbers,V Subspace:Suppose andare subspace of V,then v2 is also a subspace of V +2 is also a subspace of V1. Vector Space (or Linear Space ), if it satisfies with 1) Sums 1 2 2 1 v  v  v  v 1 2 3 1 2 3 v  ( v  v )  ( v  v )  v v  (  v )  (  v )  v  0 v  0  0  v  v for all & in v1 v2 V for all & in v1 , v 2 v3 V v ,  v in V v  V 2) Products (a) r ( r v ) ( r r ) v are real numbers, 1 2 1 2    1 2 r , r v  V (b) is a real number, 1 2 1 2 r  ( v  v )  r v  r v v 1 , v 2  V r r v r v r v 1 2 1 2 (c) (  )    1 2 are real numbers, r , r v  V Subspace: Suppose and are subspace of , then v1 v2 V v 1  v 2 is also a subspace of V v 1  v 2 is also a subspace of V Chapter 3 3 3.1 Mathematic review