0

I'm reading convex optimization by Boyd and I have a problem with normal of a hyperplane

how many normal can we assume for a hyperplane at just one point?

is it true that we can assume many vectors with different length (and all of them can be normal) at just one point so we have many normal for a hyperplane

eHH
  • 463
  • 1
  • 4
  • 14
  • 2
    Yes, there are many different ones up to scalar multiplication, so the notion of the normal is not very well-defined. However, once you specify a unit normal, then in Euclidean space, any hyperplane only has two of these (unit normals) at a given point. – ah11950 Mar 21 '14 at 11:59
  • Hyperplane has two unit normal or two normal ? – eHH Mar 21 '14 at 12:02
  • Edited for clarity. Unit normals. – ah11950 Mar 21 '14 at 12:03
  • When I teach multi-variable caclulus I introduce the notion of normal line to a plane. A direction vector for the line is then normal to the plane, and direction vectors are highly non-unique. – dezign Mar 21 '14 at 12:27
  • A hyperplane has two unit normals, one for each side of the plane. A hyperplane divides a space into two halfspaces, each of which can be associated with one of the two unit normals. – Michael Grant Mar 21 '14 at 12:30

1 Answers1

2

A hyperplane has two unit normals, one for each side of the plane. A hyperplane divides a space into two halfspaces, each of which can be associated with one of the two unit normals. -- Michael Grant