Mixed tensor: Difference between revisions
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A mixed tensor of type <math> \begin{pmatrix} M \\ N \end{pmatrix} </math>, with both ''M'' > 0 and ''N'' > 0, is a tensor which has ''M'' contravariant indices and ''N'' covariant indices. Such tensor can be defined as a [[linear operator|linear function]] which maps an ''M+N''-tuple of ''M'' [[one-form]]s and ''N'' [[vector]]s to a [[scalar]]. |
A mixed tensor of type <math> \begin{pmatrix} M \\ N \end{pmatrix} </math>, with both ''M'' > 0 and ''N'' > 0, is a tensor which has ''M'' contravariant indices and ''N'' covariant indices. Such tensor can be defined as a [[linear operator|linear function]] which maps an ''M+N''-tuple of ''M'' [[one-form]]s and ''N'' [[vector]]s to a [[scalar]]. |
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==See also== |
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* [[Tensor (intrinsic definition)]] |
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Revision as of 01:12, 11 July 2005
In tensor analysis, a mixed tensor is a tensor which is neither covariant nor contravariant. At least one of the indices of a mixed tensor will be a subscript (covariant) and at least one of the indices will be a superscript (contravariant).
A mixed tensor of type , with both M > 0 and N > 0, is a tensor which has M contravariant indices and N covariant indices. Such tensor can be defined as a linear function which maps an M+N-tuple of M one-forms and N vectors to a scalar.
See also
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