Mixed tensor

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 ${\begin{pmatrix}M\\N\end{pmatrix}}$, 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.