List questions from vector-space-isomorphism

Published on 22 Mar 2026 - 21:35

104

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if $T$ is isomorphism, how can I prove that $[T^{-1}]_B=[T]_B^{-1}$ for any base $B$ of $V$?

Published on 22 Mar 2026 - 13:16

110

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Proofs on Isomorphism Problems

Published on 22 Mar 2026 - 20:42

143

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Basis of vector spaces in perfect pairing

Published on 20 Mar 2026 - 4:23

89

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Linear isomorphism of quotient spaces

Published on 23 Mar 2026 - 7:02

100

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$V$ and $\mathcal{L}(\mathbf{F},V)$ are isomorphic

Published on 22 Mar 2026 - 18:49

950

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Isomorphic Hilbert spaces iff they have the same dimension

Published on 22 Mar 2026 - 21:20

808

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Vector space isomorphic to direct sum

Published on 21 Mar 2026 - 19:18

203

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Trying to find the dimension of a vector space...

Published on 22 Mar 2026 - 17:02

385

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$V^*$ is isomorphic to the direct product of copies of $F$ indexed by $A$

Published on 23 Mar 2026 - 9:18

44

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l^-1∈L(w;v) is bijective?

Published on 22 Mar 2026 - 21:22

1.7k

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Prove that $V$ is isomorphic to $W \times V/W$.

Published on 17 Mar 2026 - 17:24

422

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Finding an isomorphism between two vector spaces

Published on 17 Mar 2026 - 14:28

3.3k

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Isomorphism between quotient space $X/M$ and the orthogonal complement of $M$.

Published on 17 Mar 2026 - 17:37

430

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To show an operator is an isomorphism

Published on 17 Mar 2026 - 8:32

List Question

Showing that $ \text{Ind}_H^G W \cong \text{Ind}_K^G(\text{Ind}_H^K W)$

if $T$ is isomorphism, how can I prove that $[T^{-1}]_B=[T]_B^{-1}$ for any base $B$ of $V$?

Proofs on Isomorphism Problems

Basis of vector spaces in perfect pairing

Linear isomorphism of quotient spaces

$V$ and $\mathcal{L}(\mathbf{F},V)$ are isomorphic

Isomorphic Hilbert spaces iff they have the same dimension

Vector space isomorphic to direct sum

Trying to find the dimension of a vector space...

$V^*$ is isomorphic to the direct product of copies of $F$ indexed by $A$

l^-1∈L(w;v) is bijective?

Prove that $V$ is isomorphic to $W \times V/W$.

Finding an isomorphism between two vector spaces

Isomorphism between quotient space $X/M$ and the orthogonal complement of $M$.

To show an operator is an isomorphism

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