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Prove The Following Properties Of Orthogonal Complements Let R, S ⊆ Rn. Then 1 S^⊥ ⊆ R^n. 2 S ⊕S^⊥ = R^n. 3 (S^⊥)^⊥ = S. 4 R ⊆ S If And Only If S^⊥ ⊆ R^⊥. 5 (R+S)^⊥ = R^⊥∩S^⊥. 6 (R ∩ S)^⊥ = R^⊥ +S^⊥.

匿名用户 最后更新于 2021-12-01 19:07 数学类Mathematics

Prove the following Properties of Orthogonal Complements Let R,S ⊆ Rn. Then
1 S^⊥ ⊆ R^n.
2 S ⊕S^⊥ = R^n.
3 (S^⊥)^⊥ = S.
4 R ⊆ S if and only if S^⊥ ⊆ R^⊥.
5 (R+S)^⊥ = R^⊥∩S^⊥.
6 (R ∩ S)^⊥ = R^⊥ +S^⊥.


Theorem 1 Let R,S CR”. Then O SI CR”. Sest=R”. O (S)' = S. @ RCS if and only if St CR-, 6 (R+I+=Rtnet. 6 (ROS)+=R++$.

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