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    Hyperplane

    Basic definition

    A hyperplane is a generalization of a plane to more than two dimensions.

    Detailed definition

    Let a_1, a_2, ..., a_n be scalars not all equal to 0. Then the set S consisting of all vectors X = [x_1 x_2 ⋮ x_n] in R^n such that a_1 x_1 + a_2 x_2 + ... + a_n x_n = c for c a constant is a subspace of R^n called a hyperplane.

    Related terms

    plane | subspace

    Related Wolfram Language symbol

    Hyperplane

    Educational grade level

    high school level

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