| 1. | Then the standard dot product is a symmetric bilinear form,.
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| 2. | In other words, the bilinear form determines a linear mapping
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| 3. | The matrix is read off from the explicit bilinear form as
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| 4. | It has 3 sublattices of index 2 that are integral bilinear forms.
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| 5. | When is the identity, then is a bilinear form.
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| 6. | Thus, the sesquilinear form can be viewed as a bilinear form.
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| 7. | Then the function defined by is a symmetric bilinear form.
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| 8. | This bilinear form then transform tensorially under a reflection or a rotation.
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| 9. | As such it is a nondegenerate symmetric bilinear form, a type tensor.
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| 10. | On, define a nondegenerate alternating bilinear form by.
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