Vector spaces

  • Thread starter garyljc
  • Start date
  • #1
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Just have a question
if U,V and W are over the same field K
does it mean that dim U = dim V = dim W ?
 

Answers and Replies

  • #2
Ben Niehoff
Science Advisor
Gold Member
1,883
162
No.

For example, [itex]R^2[/itex] and [itex]R^3[/itex] are both over the same field R, but R^2 has dimension 2 and R^3 has dimension 3.
 

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