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Added of note on the norm used in the definition, and emphasized that the definition must be verified for any path used with an example. |
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Such functions are applied in [[control theory]].
Notice that the norm used in the definition can be any norm defined on <math> \mathbb{R}^n </math>, and that the behavior of the function along the axes does not necessarily reveal that it is radially unbounded or not; i.e. that to be radially unbounded the condition must be verified along any path that results in:
:<math>\|x\| \to \infty \, </math>
For example the function
:<math>\ f(x)= (x_1-x_2)^2 \, </math>
is not radially unbounded since along the line <math> x_1 = x_2 </math>, the condition is not verified
==References==
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