This is a purely algebraic concept. Although the concept of plane with 3 dimensions and below can have actual correspondence, there is no actual correspondence in high-dimensional space, so there is no need to think about its geometric image, although it has application in theory.

N-dimensional hyperplane in high-dimensional Euclidean space satisfies a (1) * x (1)+a (2) * x (2)+a (3) * x (3)+...+a (n) x (n)+b = 0.

A collection of points, (

x( 1)，x(2)...x(n))

As for Euclidean space, there is also a complete definition, so I won't talk about it here.