real orthogonal matrices do rotations

(Av) . (Aw) = v’ A’ A w = v’ w = v . w

So dot products are the same, before and after transformation. That means lengths and angles are the same.

Is this a rotation? Might it instead be a translation? No:

A0 = 0

Center is the same.

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there seems to be some kind of gradient from trashy to pretentious going from Trump’s “Never Give Up”, to Obama’s “The Audacity of Hope,” to Xi’s “The Governance of China.” Just looking at the titles I mean.

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I thought this was a dumb ass book title until I opened it up and found that it was actually a collection of four essays, each about a different hut

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My aunt gave me a book of Allen Ginsburg poems. I read some of Howl and said, it sounds like Allen Ginsburg’s friends got in a lot of trouble.

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adzolotl replied to your post “real orthogonal matrices do rotations”

Might be a reflection!

No way.

Shit.

Really?

OK if i’ve got v, and rotate up by θ counterclockwise and you've got w. And then you do a reflection and you've got Av and Aw.

Then, starting at Av, you rotate by θ clockwise to get Aw.

So i'm gonna go ahead and say that v . w = - (Av . Aw)

So no, it can't be a reflection.

Right?