作者t0444564 (艾利欧)
看板Math
标题[微积] Marsden 高微 第一章第20题 关於orthogonal正交
时间Fri Dec 31 03:34:49 2010
题目是:
Let S and T be nonzero orthogonal subspaces of R^n. Prove that if S and T are
orthogonal complements (that is, S and T span all of R^n), then S交集T={0}
and dim(S) + dim(T) = n , where dim(S) denotes dimension of S. Give examples
in R^3 of nonzero orthogonal subspaces for which the condition dim(S) + dim(T)
= n holds and examples where it fails. Can it fail in R^2?
打的有点冗长,而且有学过一点线性代数就会觉得太trivial.
结果完全不知道怎麽证(或说我可以使用甚麽事实去证?)
至於Examples , 我看不太懂他想要我给甚麽样的例子(应该说,不懂题意.)
甚麽是失败在R^2?(是说正交的情况失败在R^2吗?,那只有S和T同方向才失败吧?!)
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1F：→ mzhrqoc01 :例子应该是要说明dim(S) + dim(T) = n必须要有S and 12/31 03:54
2F：→ mzhrqoc01 :T span all of R^n的条件，但在R^2这个条件自然成立 12/31 03:55