Let , , ..., be Scalars not all equal to 0. Then the Set consisting of
all Vectors

in such that

is a Subspace of called a hyperplane. More generally, a hyperplane is any co-dimension 1 vector Subspace of a Vector Space. Equivalently, a hyperplane in a Vector Space is any Subspace such that is 1-dimensional. Equivalently, a hyperplane is the Kernel of any Nonzero linear Map from the Vector Space to the underlying Field.

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1999-05-25