Let $V$ be an infinite dimensional vector space and $A$ be a subspace of $V$. Is there always an orthogonal complement of $A$ in $V$? If not, is there a counter-example? Thank you very much.
Orthogonal complement in an infinite dimensional vector space.
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linear-algebra
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0Once you fix$a$basis $(b_i)$ (like a Hammel basis), you can get a bilinear form, hence an orthogonality concept, simply define $\langle b_i,b_j\rangle := \delta_{ij}$. – 2012-11-19