I want show that a line ( which is defined as $$ L = \{ x_0 + \lambda d : \lambda \in \mathbb R^n \} $$ ) is a polyhedral set and for that I need to prove that we can show any line in R^n by a fine number of linear inequalities .


Any $n-1$-hyperplane can be written as a linear equation of $n$ variables.

Any linear equation can be written as two matching inequalities with opposite sense.

Any $m-k$-hyperplane can be written as the intersection of $k+1$ $m$-hyperplanes.

  • $\begingroup$ Where can I find the proof ? $\endgroup$ – Pegi Oct 19 '19 at 18:49
  • $\begingroup$ The dimension of a hyperplane is always one less than the dimension of the space then what’s a m-k hyperplane ? $\endgroup$ – Pegi Oct 19 '19 at 19:30

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