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I am trying to understand the hyperplane of the SVM algorithm. My problem is that different sources state different equations.

Which equation is the right one and if both are right, why?

Furthermore, I thought the normal form of a plane looks like this:

$$ w\cdot x + w\cdot a = 0.$$

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They are equivalent. The interpretation of $b$ in the first equation is the same as $-b$ in the second equation. –  user10525 Dec 24 '12 at 1:28
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Just to get it right. That means that the dot product of w⋅a of the third equation equals +/-b? where b is the shift of the plane? –  user18075 Dec 24 '12 at 10:06
    
Indeed, note that this is related to the different parameterisations of the line/plane equations (point-slope, two points, slope-intercept ...) –  user10525 Dec 24 '12 at 11:17

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