\[\mathbb{R}^n\]
, a hyperplane in \[\mathbb{R}^n\]
is an \[n-1\]
dimensional subspace.A hyperplane is
\[\mathbb{R}\]
(of dimension 1) is a point (of dimension 0).A hyperplane is
\[\mathbb{R}^2\]
(of dimension 2) is a line (of dimension 1).Example:
\[2x_1+3x_2=6\]
A hyperplane is
\[\mathbb{R}^3\]
(of dimension 3) is a plane (of dimension 2).Example:
\[2x_1+3x_2+4x_3=12\]
A hyperplane is
\[\mathbb{R}^n\]
(of dimension n) is a plane (of dimension n-1).Example:
\[2x_1+3x_2+...+4x_n=20\]