My lecturer is prone to making mistakes in his slides and I was wondering if this was one of them.
edit: included the whole slide to give more context
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It is impossible to tell without more context. – copper.hat Dec 13 '16 at 14:28
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What's wrong with the usual interpretation of the sign function? – Ant Dec 13 '16 at 14:35
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1@Ant I didn't know about the existence of the sign(signum) function until you just referred to it. Thanks for clearing that up, albeit inadvertently. – stefanhorne Dec 13 '16 at 14:40
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It means tha the sign of $f$ (1, 0, or -1) is the same as the sign of $\cos \theta$.
marty cohen
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Given the diagrams and the goal of class assignment, I would say that here 'sign' means literally the algebraic sign of the value - i.e '+' (positive) or '-' (negative). I.e the vector is assigned to class A when the angle is less than 90 degrees, which occurs when the cosine of the angle is positive; alternately, the vector is assigned to class B when the angle is greater than 90 degrees [and less than 180 degrees, which is implicit from the way the vector is derived], which occurs when the cosine of the angle is negative. [the case of exactly 90 degrees isn't handled, but the chances of such a vector are effectively zero]
PMar
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