If-a-vector-v-exists-in-n-dimensions-v-R-n-Can-there-exist-a-complex-dimension-s-

Question Number 6932 by FilupSmith last updated on 03/Aug/16

If a vector v exists in n dimensions :

v \in R^{n}

Can there exist a complex dimension (s) ?

Commented by nburiburu last updated on 04/Aug/16

y o u m e a n i f v \in R^{n} \Rightarrow v \in C^{n} ?

r e a l l y, i t c o u l d b e e x i s t a f u n c t i o n t h a t

t r a n s f o r m v f r o m o n e s p a c e t o t h e o t h e r

b u t t h e y a r e d i f f e r e n t d i m e n s i o n s p a c e s

s o y o u c a n n e v e r s a y t h e y a r e t h e s a m e

(a s e q u a l v e c t o r), b u t y o u c a n s a y t h e y a r e

t h e s a m e (b y a p p l y i n g a l i n e a r t r a n s f o r m a t i o n)