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Isomorphism and dimension exercise clarification.

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#linear-algebra #linear-transformations #vector-space-isomorphism
350
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Linear map $L \neq O$ having trivial image only at $L^2=L \circ L$

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#linear-algebra #vector-spaces #linear-transformations #vector-space-isomorphism
197
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Isomorphism of X to itself.

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#linear-algebra #vector-space-isomorphism
2.9k
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Is $V$ isomorphic to direct sum of subspace $U$ and $V/U$?

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#linear-algebra #proof-verification #vector-space-isomorphism
106
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Is $ f(A) = A + 2A^{T} $ an isomorphism of $ \mathbb R^{5,5} $ onto itself?

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#linear-algebra #matrices #vector-space-isomorphism
70
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$ \operatorname{Ker}TR = \{0\}$ but $ \operatorname{Ker}T \not= \{0\}$ where $R$ is an isomorphism?

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#linear-algebra #linear-transformations #vector-space-isomorphism
31
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How to show isometry of the space through plane?

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#isometry #vector-space-isomorphism
186
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Endomorphism on polynomial vector space $\mathbb{R}_3[x]$

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#linear-algebra #vector-spaces #eigenvalues-eigenvectors #vector-space-isomorphism
517
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Banach spaces and isomorphism between dual spaces

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#banach-spaces #dual-spaces #vector-space-isomorphism
53
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Linear algebra, proof that it's an isomorphism.

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#linear-algebra #vector-space-isomorphism
55
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Show that an operator with certain properties is an isomorphism

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#functional-analysis #hilbert-spaces #spectral-theory #vector-space-isomorphism
48
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Let $T: V \rightarrow W$ be a vector space isomorphism. Prove that the $T$ maps proper subspaces to proper subspaces.

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#vector-spaces #vector-space-isomorphism
386
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If $T\in B(X,Y)$ and $T$ is bijective is $T^*$ also bijective?

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#functional-analysis #dual-spaces #vector-space-isomorphism
333
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Isomorphisms and Linear Maps

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#linear-algebra #vector-spaces #linear-transformations #vector-space-isomorphism
50
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Proof or counterexample for isomorphism of group representations

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#representation-theory #lie-groups #vector-space-isomorphism

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