The discussion clarifies that the angle between two 7-dimensional vectors can indeed be calculated, despite initial skepticism regarding their comparability. It emphasizes that vectors are one-dimensional entities, regardless of the dimensionality of the space they inhabit. The angle is determined within the plane spanned by two non-collinear vectors, which is applicable even in higher dimensions. Misunderstandings about the concept of vectors "occupying" dimensions are addressed, reinforcing the mathematical principles involved.
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First, I don't understand what you mean by a vector "occupying" 7 dimensions. A vector is, pretty much by definition, a one dimensional object, no matter what the dimension of the underlying space. Perhaps that is your misunderstanding. You may be think of the vector as "taking up" the entire space. That is not true in 7 dimensions any more than it is true in 3 dimensions. You are talking about vector s in 7 dimensions, not "occupying" 7 dimensions.robertjford80 said:Apparently you can calculate the angle between two vectors even when they occupy say 7 dimensions. I have trouble believing that. To me if a vector occupies 7 dimensions than it is incommensurable with another vector occupying 7 dimensions.