[線代] dim(W1∩W2) = dim(W1)
題目:
Let W1 and W2 be subspaces of a finite-dimensional vector space V.
Determine necessary and sufficient conditions on W1 and W2 so that
dim(W1∩W2) = dim(W1).
解答:
https://imgur.com/XL3SBrM
問題:
1.
v !∈ span(β)?
beta是W1的basis，v為什麼不屬於span(β)?
2.
v !∈ span(β) and hence β∪{v}would be a independent set with size greater
than that of β.這是定理ok.
但不理解這樣就結論dim(W1∩W2) = dim(W1)?
謝謝!
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