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Why is the metric of a Riemannian manifold required to be symmetric?

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#differential-geometry #riemannian-geometry #bilinear-form
183
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What is the dual space of the tensor product of U' and V'?

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#linear-algebra #tensor-products #dual-spaces #bilinear-form
115
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Signature and Orthogonal Basis of Symmetric Bilinear Form

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#orthogonality #bilinear-form #change-of-basis #gram-schmidt
61
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Properties of symmetric bilinear form

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#linear-algebra #matrices #positive-definite #bilinear-form
27
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Question regarding the unitary group $U(p,q)$ of a definite non-deg. hermitian form

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#linear-algebra #group-theory #solution-verification #bilinear-form
71
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Terminology: how do we call a vector space equipped with a symmetric bilinear form over a general field?

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#linear-algebra #abstract-algebra #terminology #bilinear-form
54
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signature of biliner form and the signature on the induced Hermitian form

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#real-analysis #linear-algebra #matrices #bilinear-form
76
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How to find out the index of the given quadratic form?

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#linear-algebra #quadratic-forms #bilinear-form
82
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Is there a name for a vector space together with a bilinear form?

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#terminology #bilinear-form
123
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$ G $-invariant symmetric bilinear map and trivial subrepresentation of symmetric square

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#group-theory #representation-theory #bilinear-form #symmetric-algebra
325
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Diagonalization of a symmetric bilinear form over the integers

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#linear-algebra #matrices #symmetric-matrices #positive-definite #bilinear-form
150
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Determining an integral positive-definite symmetric matrix is diagonalizable over $\Bbb Z$

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#linear-algebra #matrices #diagonalization #positive-definite #bilinear-form
55
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Existence of the 'matrix' associated to a form

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#linear-algebra #bilinear-form
61
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Searching for a proof or reference of a statement.

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#linear-algebra #bilinear-form
262
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Are two quadratic forms equivalent over $\mathbb{Q}$

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#linear-algebra #equivalence-relations #matrix-rank #quadratic-forms #bilinear-form

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