Hyperspace - Illustration

Here you can learn how to visualize a hyperspace in    or  .

   A hyperspace in    is a line through the origin
Thus the red line in the picture below is a hyperspace. We characterize it as the collection of all those vectors x which are perpendicular to the green vector n, called a normal vector of the hyperspace.

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   A hyperspace    in    is a plane through the origin

The blue arrow n, is called a normal vector of the hyperspace because it is perpendicular to all those vectors which belong to the hyperspace  . The second plane in this picture (horizontal) is only there to provide visual reference points.

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   If  > 3, we cannot visualize a hyperspace in  . Still we can imagine it to be an object which plays in    a role analogous to that of a line through the origin in    or analogous to that of a plane through the origin in  .

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Return to the main document on hyperplanes.