Antisymmetric ones change sign upon changing the order of two components.
The comma and semicolon derivatives act on these. Absolute ones are relative ones of weight zero. One manipulation technique of these is called index gymnastics. Antisymmetric ones change sign upon changing the order of two components. In Lorentzian spaces, the covariant and contravariant order of them are not the same, unlike in three-dimensional space. These can be contracted to produce vectors. The product of two of these is in general a new one with rank equal to the sum of their ranks. For 10 points, name these generalizations of scalars and vectors; mathematical objects generally representable as matrices.
The comma and semicolon derivatives act on these. Absolute ones are relative ones of weight zero.
{tensors} [prompt on {matrices}]