Hyperplanes?

[Asimov Pupil]

can someone please introduce me to Hyperplanes. thank you

[Dave]

The more pertanent question is, what do you want to know about them?

[ydoaPs]

would they be like a full rectangular prism?

[Dave]

According to MathWorld, a hyperplane can be more than 4-dimensional (it's an n-dimensional object), so you can't really say what it would "look" like.

[ydoaPs]

eh, i was thinking of 3 dimensions.

[Dave]

How would you have a hyperplane in 3 dimensions? Do you mean the projection onto 3 dimensions?

[ydoaPs]

plane is 2-d, right? i added a dimension.

[Dave]

No, a plane is 3-dimensional. A line is 2-dimensional

[matt grime]

A hperplane in any vector space of dimension n is an n-1 dimensional subspace, ie a line in R^2, a plane (through the origin) in R^3, a copy of R^3 in R^4. Sometimes that is simplified to any subspace of "codimension 1" which allows for infinite dimensional definitions as well. The simplest examples that occur "naturally" are in hilbert spaces, or an inner product space, where we can use any element z to define a hyperplane as the {x : <x,z>=0}