Is there a general rule to simplify things like $<x,y> - <x,z>$ or generally $<.,.> \pm <.,.>$
I cant find anything in my notes that talks about this.
2026-04-24 13:25:21.1777037121
"Adding" inner products
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By definition of bilinearity, $\langle x,y\rangle - \langle x,z\rangle = \langle x,y-z\rangle$.
On the other hand in general there is no formula for $\langle a,b\rangle \pm \langle c,d\rangle$.