Must these two vector spaces always be isomorphic?
0
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Suppose $V$ and $W$ are vector spaces over $mathbb{Q}$ and the cardinality of $V$ is the same as the cardinality of $W$. Must $V$ and $W$ be isomorphic?
linear-algebra
asked Jan 13 at 16:54
FortoxFortox
6718
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add a comment |
0
$begingroup$
Suppose $V$ and $W$ are vector spaces over $mathbb{Q}$ and the cardinality of $V$ is the same as the cardinality of $W$. Must $V$ and $W$ be isomorphic?
linear-algebra
asked Jan 13 at 16:54
FortoxFortox
6718
$endgroup$
4
$begingroup$
What is the cardinality of $mathbb{Q}?$ What is the cardinality of $mathbb{Q}^2?$
$endgroup$
– saulspatz
Jan 13 at 17:01
2
$begingroup$
You could have two vector spaces of the same cardinality but different dimension so not isomorphic
$endgroup$
– J. W. Tanner
Jan 13 at 17:02
add a comment |
0
0
0
$begingroup$
Suppose $V$ and $W$ are vector spaces over $mathbb{Q}$ and the cardinality of $V$ is the same as the cardinality of $W$. Must $V$ and $W$ be isomorphic?
linear-algebra
asked Jan 13 at 16:54
FortoxFortox
6718
$endgroup$
Suppose $V$ and $W$ are vector spaces over $mathbb{Q}$ and the cardinality of $V$ is the same as the cardinality of $W$. Must $V$ and $W$ be isomorphic?
linear-algebra
linear-algebra
asked Jan 13 at 16:54
FortoxFortox
6718
asked Jan 13 at 16:54
FortoxFortox
6718
asked Jan 13 at 16:54
FortoxFortox
6718
asked Jan 13 at 16:54
FortoxFortox
6718
asked Jan 13 at 16:54
FortoxFortox
6718
6718
4
$begingroup$
What is the cardinality of $mathbb{Q}?$ What is the cardinality of $mathbb{Q}^2?$
$endgroup$
– saulspatz
Jan 13 at 17:01
2
$begingroup$
You could have two vector spaces of the same cardinality but different dimension so not isomorphic
$endgroup$
– J. W. Tanner
Jan 13 at 17:02
add a comment |
4
$begingroup$
What is the cardinality of $mathbb{Q}?$ What is the cardinality of $mathbb{Q}^2?$
$endgroup$
– saulspatz
Jan 13 at 17:01
2
$begingroup$
You could have two vector spaces of the same cardinality but different dimension so not isomorphic
$endgroup$
– J. W. Tanner
Jan 13 at 17:02
4
4
$begingroup$
What is the cardinality of $mathbb{Q}?$ What is the cardinality of $mathbb{Q}^2?$
$endgroup$
– saulspatz
Jan 13 at 17:01
$begingroup$
What is the cardinality of $mathbb{Q}?$ What is the cardinality of $mathbb{Q}^2?$
$endgroup$
– saulspatz
Jan 13 at 17:01
2
2
$begingroup$
You could have two vector spaces of the same cardinality but different dimension so not isomorphic
$endgroup$
– J. W. Tanner
Jan 13 at 17:02
$begingroup$
You could have two vector spaces of the same cardinality but different dimension so not isomorphic
$endgroup$
– J. W. Tanner
Jan 13 at 17:02
add a comment |
0
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4
$begingroup$
What is the cardinality of $mathbb{Q}?$ What is the cardinality of $mathbb{Q}^2?$
$endgroup$
– saulspatz
Jan 13 at 17:01
2
$begingroup$
You could have two vector spaces of the same cardinality but different dimension so not isomorphic
$endgroup$
– J. W. Tanner
Jan 13 at 17:02