Locating the quadrant having a factor on an n-sphere

Suppose I have a factor $x \in \mathbb{R}^n$ on an n-sphere. Intend I separate the n-sphere right into 4 areas (I assume this makes good sense in $n$ measurements ), just how do I recognize which area $x$ pushes?

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2019-05-07 12:18:38
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This is simply a rephrasing of ShreevastasR's solution ; no debt to me. It does make good sense to separate an $n$ - round right into quadrants, as you clarify in $\mathbb{R}^3$ : dividing by 2 coordinate aircrafts. Yet after that determining which quadrant is, as ShreevastasR claims, merely considering the indicators of the works with of $x$. If $x_1$ and also $x_2$ are both favorable, you remain in the first, $++$, quadrant ; if $x_1$ is adverse and also $x_2$ favorable, you remain in the 2nd, $-+$, quadrant. And more. If rather you dividing the round right into $2^n$ orthants, after that you take into consideration all the indicators of the works with of $x$.

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2019-05-09 05:57:26
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