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Given a collection of $n$ real number arrays of length $m$, for example:

$[r_{11},\ \dots, r_{1m}]$ $\vdots$ $[r_{n1},\ \dots, r_{nm}]$ is it possible to transform the entire collection into one equivalent complex number array of length $m$, for example, $[c_1,\ \dots, c_m]$?

Also, the solution should be the same regardless of the row order in the collection.

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    Thank you. I have a somewhat related question but I'll use another thread and try to be more precise in the description.2012-02-16

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  • Yes if $n=1$, because a real number is also a complex number.
  • Yes if $n=2$, because a pair of real numbers $r(0,k)$ and $r(1,k)$ can be represented by one complex number.
  • No if $n>2$, because there is no natural way to represent three or more real numbers as a single complex number (unnatural ways include mashing two single-precision numbers into double-precision, but this is silly, and does not go far.)