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Wedge Products with the Symplectic Form

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#linear-algebra #symplectic-geometry #vector-space-isomorphism
72
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Find out if the transformation is linear, if so, determine whether it is an isomorphism.

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#linear-algebra #vector-spaces #vector-space-isomorphism
90
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Determine whether or not the transformation is isomorphic

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#linear-algebra #vector-space-isomorphism
2k
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I need help in constructing and proving an isomorphism

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#linear-algebra #proof-writing #linear-transformations #vector-space-isomorphism
217
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Is a tensor product of maps an isomorphism iff maps themselves isomorphisms?

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#linear-algebra #tensor-products #vector-space-isomorphism
775
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How to prove that if $S: U\rightarrow V$ and $T: V\rightarrow W$ are isomorphisms, then $TS$ is also an isomorphism?

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#linear-algebra #vector-spaces #linear-transformations #vector-space-isomorphism
871
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Finite-dimensional vector space isomorphism problem

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#linear-algebra #solution-verification #vector-spaces #linear-transformations #vector-space-isomorphism
57
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Checking that $\Bbb C \cong \Bbb R^2$ as real vector spaces.

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#linear-algebra #vector-space-isomorphism
29
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A condition to a set $X$ to be a vector space

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#vector-spaces #vector-space-isomorphism
1k
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Null space isomorphic to range iff closed

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#functional-analysis #banach-spaces #vector-space-isomorphism
252
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Prove that if $A$ is a linear transformation on a finite dimensional vector space $V$, then $V\cong \mathrm{Range}(A)\oplus \mathrm{Nullspace}(A)$.

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#linear-algebra #vector-space-isomorphism
366
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Isometry and isomorphism normed spaces

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#normed-spaces #isometry #vector-space-isomorphism
104
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How to describe the vector space $\left( \frac{Z}{Im(T)} \right)^*$?

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#linear-algebra #linear-transformations #quotient-spaces #vector-space-isomorphism
2.6k
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Determinant of the matrix representation of an isomorphic linear transformation

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#linear-algebra #matrices #vector-spaces #linear-transformations #vector-space-isomorphism
158
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Prove that the conjugate transpose is bijective too

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#functional-analysis #vector-space-isomorphism #transpose

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