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Why is the symplectic group defined with a skew-symmetric matrix?

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#linear-algebra #symplectic-linear-algebra
253
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decomposition of general symplectic matrix

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#linear-algebra #symplectic-geometry #symplectic-linear-algebra
76
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Trivialization of a path of tamed almost complex structures

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#linear-algebra #differential-geometry #symplectic-geometry #symplectic-linear-algebra #almost-complex
133
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Is every almost complex structure tame up to sign?

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#multilinear-algebra #symplectic-linear-algebra #almost-complex
1.2k
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$2$ out of $3$ property of the unitary group

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#multilinear-algebra #symplectic-linear-algebra #almost-complex
469
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Inclusion $O(2n)/U(n)\to GL(2n,\mathbb{R})/GL(n,\mathbb{C}) $

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#linear-algebra #algebraic-topology #homotopy-theory #symplectic-geometry #symplectic-linear-algebra
1.1k
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Relationship between symplectic forms and skew-symmetric matrices

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#linear-algebra #symplectic-linear-algebra
54
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linear subsets of linear space

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#vector-spaces #symplectic-linear-algebra
3.1k
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Understanding the relationship between $Sp(n)$ and $Sp(2n,\mathbb{C})$

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#group-theory #symplectic-linear-algebra
5.1k
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Is it true that the whole space is the direct sum of a subspace and its orthogonal space?

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#linear-algebra #geometry #quadratic-forms #bilinear-form #symplectic-linear-algebra
32
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Find an abelian subgroup of $GL(2n, q)$ of special order

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#group-theory #lie-groups #abelian-groups #symplectic-linear-algebra
70
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find a special element of $Sp(2n,q)$

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#abstract-algebra #group-theory #symplectic-linear-algebra
141
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Understanding a sentence in a paper.

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#linear-algebra #symplectic-linear-algebra
8.2k
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What is the dual matrix (of a sample covariance matrix)?

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#linear-algebra #matrices #probability-distributions #random-matrices #symplectic-linear-algebra
79
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Find this symplectic transforming matrix

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#linear-algebra #matrices #matrix-decomposition #bilinear-form #symplectic-linear-algebra

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