What are $y^+$ and $y^-$ supposed to represent? $y$ is a vector.
If y is a vector, what do y superscript + and y superscript - mean?
2
$\begingroup$
linear-algebra
terminology
-
7Hard to say unless you give us some further context. – 2011-03-22
1 Answers
6
As lhf points out, it depends on what context you are using these.
One possible answer which I have seen is $y^{+}$ is a vector whose elements are same as $y$ if the corresponding element in $y$ is positive and is zero if the corresponding element in $y$ is negative. Similarly, $y^{-}$ is a vector whose elements are same as $y$ if the corresponding element in $y$ is negative and is zero if the corresponding element in $y$ is positive.i.e.
If $y \in \mathbb{R}^{n \times 1}$, then
$y^{+} \in \mathbb{R}^{n \times 1}$ with $y^{+}(i) = \max(y(i),0)$
and
$y^{-} \in \mathbb{R}^{n \times 1}$ with $y^{-}(i) = \min(y(i),0)$
Hence, $y(i) = y^{+}(i) + y^{-}(i)$
-
1@Matt: Yes. Some people use that convention as well i.e. $y^{-}(i) = \max(-y(i),0)$ so that both $y^{+}$ and $y^{-}$ are non-negative and then we get $y(i) = y^{+}(i) - y^{-}(i)$ – 2011-03-22