Question

Why are bilinear maps represented as members of the tensor space $V^\otimes V^$ opposed to just members of the tensor space $V\otimes V$?

score 2.4k · Answer 1 · 2026-03-20 10:57:55

2.4k

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Why are bilinear maps represented as members of the tensor space $V^\otimes V^$ opposed to just members of the tensor space $V\otimes V$?

Published on 20 Mar 2026 - 10:57

score 261 · Answer 2 · 2026-03-21 23:27:42

261

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Milnor's octahedron

Published on 21 Mar 2026 - 23:27

score 101 · Answer 3 · 2026-03-17 11:35:00

101

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Difference between $T^{i}_{\;\;j}$ and $T_i^{\;\;j}$?

Published on 17 Mar 2026 - 11:35

score 1.2k · Answer 4 · 2026-03-22 20:16:19

1.2k

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Square root of a matrix (or a 2nd order tensor)

Published on 22 Mar 2026 - 20:16

score 137 · Answer 5 · 2026-03-22 15:36:29

137

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Restriction of a tensor to a submanifold

Published on 22 Mar 2026 - 15:36

score 57 · Answer 6 · 2018-02-11 03:15:46

57

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The proof of $\frac{\partial g_j}{\partial x_i} g_i = \frac{\partial}{\partial x_i} \Big(\frac{1}{2} |\vec{g}|^2 \delta_{ij} \Big) $.

Published on 11 Feb 2018 - 3:15

score 6.4k · Answer 7 · 2026-03-22 16:57:56

6.4k

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Partial derivative of metric tensor help

Published on 22 Mar 2026 - 16:57

score 175 · Answer 8 · 2026-03-16 21:38:09

175

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Simplifying tensor equation

Published on 16 Mar 2026 - 21:38

score 523 · Answer 9 · 2026-03-20 13:08:47

523

Views

Image of Young symmetrizer on tensor product decomposition

Published on 20 Mar 2026 - 13:08

score 1.1k · Answer 10 · 2026-03-23 23:08:50

1.1k

Views

Cofactor expression with Levi Civita symbol

Published on 23 Mar 2026 - 23:08

score 193 · Answer 11 · 2026-03-19 17:03:21

193

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Index Notation, Multiplying a 3rd order tensor with a 2nd order tensor

Published on 19 Mar 2026 - 17:03

score 544 · Answer 12 · 2026-03-20 08:29:36

544

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Nijenhuis tensor in local coordinates

Published on 20 Mar 2026 - 8:29

score 594 · Answer 13 · 2026-03-22 19:03:13

594

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Christoffel Symbols for elliptic coordinate system

Published on 22 Mar 2026 - 19:03

score 345 · Answer 14 · 2026-03-22 13:11:12

345

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Second derivative in coordinate invariant form

Published on 22 Mar 2026 - 13:11

score 23 · Answer 15 · 2018-02-20 15:34:04

23

Views

Basis vectors at points other than the origin in a curvilinear coordinate

Published on 20 Feb 2018 - 15:34

List Question

Why are bilinear maps represented as members of the tensor space $V^\otimes V^$ opposed to just members of the tensor space $V\otimes V$?

Milnor's octahedron

Difference between $T^{i}_{\;\;j}$ and $T_i^{\;\;j}$?

Square root of a matrix (or a 2nd order tensor)

Restriction of a tensor to a submanifold

The proof of $\frac{\partial g_j}{\partial x_i} g_i = \frac{\partial}{\partial x_i} \Big(\frac{1}{2} |\vec{g}|^2 \delta_{ij} \Big) $.

Partial derivative of metric tensor help

Simplifying tensor equation

Image of Young symmetrizer on tensor product decomposition

Cofactor expression with Levi Civita symbol

Index Notation, Multiplying a 3rd order tensor with a 2nd order tensor

Nijenhuis tensor in local coordinates

Christoffel Symbols for elliptic coordinate system

Second derivative in coordinate invariant form

Basis vectors at points other than the origin in a curvilinear coordinate

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