Questions tagged [vector-space-isomorphism]

This tag should be used for questions about isomorphisms between vector spaces.

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$F'$ and $E'$ are isomorphic isometrically.

Let $F$ be a dense subspace of the normed space $E$. Prove that $F'$ and $E'$ are isomorphic isometrically. At first I was trying to define a function to check the isomorphism and then show that it ...
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Regular matrix and linear transformation map

Let $A$ be a matrix with dimension $n\times n$ , $B$ is a matrix with dimension $m\times m$ then if $f : R \to R$ where $R$ is the set of matrix with dimension $m\times n$ and $f(C) = ACB$ is ...
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Is C(K) a subalgebra in its bidual?

Let $C(K)$ be the Banach algebra of real-valued continuous functions on a compact Hausdorff space $K$. It is known that the bidual of $C(K)$ is again a $C(\Omega)$ space, for some compact Hausdorff ...
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Isomorphism map between $\frac{\mathbb{Z}_3[x]}{(x^2+x+2)}$ and $\frac{\mathbb{Z}_3[x]}{(x^2 + 1)}$ [duplicate]
$\frac{\mathbb{F}_3[x]}{(x^2+x+2)} \cong \frac{\mathbb{F}_3[x]}{(x^2 + 1)}$ I know $\frac{\mathbb{F}_3[x]}{(x^2+x+2)}$ and $\frac{\mathbb{F}_3[x]}{(x^2 + 1)}$ is isomorphic because they are both 2-...
Assuming the Axiom of Choice, and therefore assuming that every vector space has a Hamel basis, it isn't too hard to show that if $U$ and $V$ are vector spaces with the same dimension (i.e. their ...