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Comment by shakow

3 years ago

A subspace of dimension n-1 of a n-dimensional vector space. It is an extension of the well-known concept of a 2d-plane in a 3d-space to nd-spaces.

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shakow

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eru  3 years ago

You could also describe a hyperplane as the set of solutions of a system of linear equations.

  • shakow  3 years ago

    Or as the subspace of all the vectors are orthogonal to a given single vector, or as the subspace generated by any orthogonal basis with one base vector removed, or as the kernel of a linear form, ... – but a more visual explanation is probably better as a first foray in the question.

    • eru  3 years ago

      I agree that a more visual explanation is better in general.

      I was trying to hint how the visual explanation relates to the long vectors of numbers we actually feed our machine learning contraptions with. Not sure I was successful.