Consider two finite dimensional linear spaces V and W. If V and W are isomorphic, then
Chapter 4, Problem 70(choose chapter or problem)
Consider two finite dimensional linear spaces V and W. If V and W are isomorphic, then they have the same dimension (by Theorem 4.2.4b). Conversely, if V and W have the same dimension, are they necessarily isomorphic? Justify your answer carefully.
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