Let's say that $V$ is an inner product space on some field $\Bbb{K}$ and $M$ is a subspace of $V$. If $M^{\perp}$ is the orthogonal complement of $M$ with respect to the inner product, can I make the statement that
$$ V=M\oplus M^{\perp} $$ if the dimension of $V$ is not specified to be finite, or even countable? In other words, is the direct sum well defined between orthogonal subspaces in an infinite-dimensional vector space?