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Old 04-20-2013, 05:51 PM
marek marek is offline
Join Date: Apr 2013
Posts: 31
Default Re: Homework set 3, problem 4 2013

Originally Posted by Elroch View Post
A little more completely, a vector w gives a real value \phi(x) = w.x to every point x. The points at which \phi(x) is zero form a hyperplane. The points at which \phi(x) is positive are on one side of the hyperplane, the points at which \phi(x) is negative are on the other side. Changing from w to -w, all the values of \phi(x) are multiplied by -1. As a result, the hyperplane stays the same, but the two regions defined by the sign of the value of the scalar product swap over.
So then the answer to my question was "yes?"
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