Given two vector subspaces $W_1$ and $W_2$ of an inner product space $V$, and $W_2 \subseteq W_1$, the relative complement of $W_2$ in $W_1$ is defined as $W_1 \cap W_2^\perp$, and some book uses the notation $W_1 - W_2$.
But the notation $W_1-W_2$ is more commonly used to represent $\{w_1 - w_2: \forall w_1 \in W_1, w_2 \in W_2\}$, which is $W_1$ here because $W_2 \subseteq W_1$.
Since I can't figure out, I wonder if there is some connection between the two definitions: relative complement and subtraction between two subspaces? Thanks.
In set theory, for two sets $A$ and $B$ we we have $A \cap B^c = A \backslash B = A - B$.
There is no relationship between the relationship you stated.
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