Dears

could you help for solving the following question:

Let V be a finite-dimensional inner product space. If A and B are subspace of V, prove that

(A ⋂ B)^{┴}= A^{┴ }+ B^{┴}

where ┴ denotes to the orthogonal complement

Best regards

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- May 21st 2012, 06:57 AMraedThe orthogonal complement of the intersection
Dears

could you help for solving the following question:

Let V be a finite-dimensional inner product space. If A and B are subspace of V, prove that

**(A ⋂ B)**^{┴}= A^{┴ }+ B^{┴}

where ┴ denotes to the orthogonal complement

Best regards - May 21st 2012, 06:59 AMraedRe: The orthogonal complement of the intersection
note that E

^{ ┴}={ y in V : <x,y>=0 , for all x in E}