# How can serial manipulator have unique condition number for given end effector position?

I am reading about Condition Number which is considered as measure of manipulability of robotic arm, it is defined as

$$k = \parallel J \parallel \parallel J^{-1} \parallel$$ Where, $$\parallel J \parallel = \sqrt {tr(JNJ^{T})}$$ How this can be a unique value for given end effector location, as manipulator can reach a point in workspace with different joint variable values, which in turn will change Jacobian value ?

Reference Paper: Comparative study of performance indices for fundamental robot manipulators Serdar Kucuka,1, Zafer Bingulb,

• Condition number gives a measure of invertibility in general for linear operators. Intuitively it gives the amount of error amplification of errors through the operation. – daaxix Oct 19 '17 at 11:19