Question Number 6932 by FilupSmith last updated on 03/Aug/16
$$\mathrm{If}\:\mathrm{a}\:\mathrm{vector}\:\boldsymbol{{v}}\:\mathrm{exists}\:\mathrm{in}\:{n}\:\mathrm{dimensions}: \\ $$$$\boldsymbol{{v}}\in\mathbb{R}^{{n}} \\ $$$$\mathrm{Can}\:\mathrm{there}\:\mathrm{exist}\:\mathrm{a}\:\mathrm{complex}\:\mathrm{dimension}\left(\mathrm{s}\right)? \\ $$
Commented by nburiburu last updated on 04/Aug/16
$${you}\:{mean}\:{if}\:{v}\in\mathbb{R}^{{n}} \:\Rightarrow{v}\in\mathbb{C}^{{n}} ? \\ $$$${really},\:{it}\:{could}\:{be}\:{exist}\:{afunction}\:{that} \\ $$$${transform}\:{v}\:{from}\:{one}\:{space}\:{to}\:{the}\:{other} \\ $$$${but}\:{they}\:{are}\:{different}\:{dimension}\:{spaces} \\ $$$${so}\:{you}\:{can}\:{never}\:{say}\:{they}\:{are}\:{the}\:{same} \\ $$$$\left({as}\:{equal}\:{vector}\right),\:{but}\:{you}\:{can}\:{say}\:{they}\:{are} \\ $$$${the}\:{same}\:\left({by}\:{applying}\:{a}\:{linear}\:{transformation}\right) \\ $$