For 10 points, name these generalizations of scalar and vector quantities to higher dimensions that are studied in a namesake calculus.
The dyadic product is a variety of the outer product whose result is one of these. A convenient invariant used for these objects is the trace, which is defined as the sum of its eigenvalues, and the covariance and contravariance of these objects gives rise to the superscripts and subscripts used to notate them, and the (*) Levi-Civita symbol is a representation of the permutation in this form. Their order is given by the number of unique indices in a term, while repeated indices within a term are summed by the conventions of Einstein notation. Those of the second order always possess a determinant because they must be square, while zeroth order ones are scalars and first order ones are vectors. For 10 points, name these generalizations of scalar and vector quantities to higher dimensions that are studied in a namesake calculus.
The dyadic product is a variety of the outer product whose result is one of these.
{tensor}