In tensor analysis, a mixed tensor is a tensor which is neither strictly covariant nor strictly 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 or 'valence, also written "type (M, N)", 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.
Read more about Mixed Tensor: Changing The Tensor Type
Famous quotes containing the word mixed:
“But oh, not the hills of Habersham,
And oh, not the valleys of Hall
Avail: I am fain for to water the plain.
Downward, the voices of Duty call—
Downward, to toil and be mixed with the main,
The dry fields burn, and the mills are to turn,
And a myriad flowers mortally yearn,
And the lordly main from beyond the plain
Calls o’er the hills of Habersham,
Calls through the valleys of Hall.”
—Sidney Lanier (1842–1881)