Math 2.0

Linear and multilinear algebra; matrix theory Definition

Symmetric bilinear form

Builds on Bilinear form

Definition

Let FF be a field and let VV be a vector space over FF. A bilinear form BB on VV is symmetric when B(u,v)=B(v,u)for all u,v∈V.B(u, v) = B(v, u) \qquad \text{for all } u, v \in V.

Remarks

In each basis, BB is symmetric if and only if its matrix is a symmetric matrix. The dot product on ℝn\R^n is symmetric. If the characteristic of FF is not 22, symmetric bilinear forms correspond one to one with quadratic forms.

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Vector space, definition, no evidence levelVector spacedefinitionBilinear form, definition, no evidence levelBilinear formdefinitionSymmetric bilinear form, definition, no evidence levelSymmetric bilinear fo…definition
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Further reading

  1. Web https://en.wikipedia.org/wiki/Symmetric_bilinear_form, Formal definition
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