Want site search autocompletion? See here Encountering 429 Too Many Requests errors when browsing the site? See here
Suppose n {\displaystyle n} is a positive integer. The signum vector function is a function R n → R n {\displaystyle \mathbb {R} ^{n}\to \mathbb {R} ^{n}} whose behavior in each coordinate is as per the signum function. Explicitly, it is defined as the function:
( x 1 , x 2 , … , x n ) ↦ ( sgn ( x 1 ) , sgn ( x 2 ) , … , sgn ( x n ) ) {\displaystyle (x_{1},x_{2},\dots ,x_{n})\mapsto (\operatorname {sgn} (x_{1}),\operatorname {sgn} (x_{2}),\dots ,\operatorname {sgn} (x_{n}))}
is a positive integer. The signum vector function is a function 
whose behavior in each coordinate is as per the signum function. Explicitly, it is defined as the function:
