- #1

WWGD

Science Advisor

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Just curious: what is the equation of a plane in R^n for n>3 ?

We cannot define a normal vector for n>3 , so, what do we do? I thought

of working with flat, embedded copies of R^2 . In terms of linear algebra,

I guess we could see a plane in R^n as any image of a linear map with

rank=2. In terms of geometry, maybe we need a "flat" embedding of R^2

(I am not clear how to make the term 'flat' here more precise) in R^n.

Anyone know?

Thanks.