1.let W1 and W2 be subspaces of a vector space V having dimensions m and n,where m>=n.(a)Prove that dim(W1交W2)
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1.let W1 and W2 be subspaces of a vector space V having dimensions m and n,where m>=n.(a)Prove that dim(W1交W2)
1.let W1 and W2 be subspaces of a vector space V having dimensions m and n,where m>=n.
(a)Prove that dim(W1交W2)
1.let W1 and W2 be subspaces of a vector space V having dimensions m and n,where m>=n.(a)Prove that dim(W1交W2)
(1)you have ignored an important formular:
dim(W1)+dim(W2)=dim(W1∩W2)+dim(W1+W2)
since
dim(W1+W2)≥m so dim(W1∩W2)≤n
and
dim(W1∩W2)≥1 so dim(W1+W2)<=m+n
(2)I holp you can provide a definition.I assume for any α∈W2,P(α)=0,that means W2 is the kernal of projection.
1.by the definition of projection.
2.by the definition of range and kernal
3.identity transformation,that is obviously
4.zero transformation.
这个非常难，请另请高人。不过我认识的一个人可能知道，如果你有邮箱，写上，会告诉你答案的。