query: How to show that a theorem holds for isomorphic vector spaces?
positive_passages.docid: 141843
positive_passages.text: n-dimensional vector space isomorphic to the n-th product of a field as abelian groups
negative_passages.docid: 100257
negative_passages.text: Converse to Hilbert basis theorem
negative_passages.docid: 108742
negative_passages.text: Proving commutativity of addition for vector spaces
negative_passages.docid: 93118
negative_passages.text: How to show that if two integral domains are isomorphic, then their corresponding field of quotients are isomorphic?
negative_passages.docid: 87766
negative_passages.text: Using Cayley's Theorem to find an isomorphic subgroup.
negative_passages.docid: 132491
negative_passages.text: How to show that $C=C[0,1]$ is a Banach space
negative_passages.docid: 27478
negative_passages.text: Proof that two basis of a vector space have the same cardinality in the infinite-dimensional case
negative_passages.docid: 4196
negative_passages.text: A valid proof for the invariance of domain theorem?
negative_passages.docid: 154754
negative_passages.text: Is $O_n$ isomorphic to $SO_n \times \{\pm I\}$?
negative_passages.docid: 68153
negative_passages.text: How to show that $L^p$ spaces are nested?
negative_passages.docid: 152887
negative_passages.text: Let $T : V \rightarrow V$ be a linear operator. If $T^n = O_V$ for some $n \ge 1$, prove that $I_V + T$ is an isomorphism.
negative_passages.docid: 41520
negative_passages.text: Prove that $L(V,W)$ forms a vector space
negative_passages.docid: 36980
negative_passages.text: Prove the third isomorphism theorem
negative_passages.docid: 40321
negative_passages.text: $\operatorname{Aut}(\mathbb Z_n)$ is isomorphic to $U_n$.
negative_passages.docid: 46116
negative_passages.text: Proof of the First Isomorphism Theorem for Groups
negative_passages.docid: 107687
negative_passages.text: How to prove that $U_{2^n}$ is isomorphic as group to $\mathbb Z_2 \times \mathbb Z_{2^{n-2}}$ for $n \ge 3$?
negative_passages.docid: 145462
negative_passages.text: On the canonical isomorphism between $V$ and $V^{**}$