Definition of (not necessarily orthogonal) projection onto a component of a direct sum

Created almost 9 years ago, updated about 8 hours ago

If $V=U\oplus W$, define the projection onto $U$ along $W$ by $P(u+w)=u$. Unique decomposition makes this well-defined and linear, with $P^2=P$, range $U$ and kernel $W$. It is orthogonal iff $W=U^\perp$. Other complements produce oblique projections.

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