contravariant tensor

[¦kän·trə′ver·ē·ənt ′ten·sər]

(mathematics)

A tensor with only contravariant indices.

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([dagger]) The contravariant tensor [g.sup.[alpha][beta]], determined by the main property [g.sub.[alpha][sigma]][g.sup.[sigma][beta]] = [[delta].sup.[beta].sub.[alpha]] of the fundamental metric tensor as ([g.sup.(0).sub.[alpha][sigma]] + [[zeta].sub.[alpha][sigma]]) [g.sup.[sigma][beta]] = [[delta].sup.[beta].sub.[alpha]], is [g.sup.[alpha][beta]] = [g.sup.(0)[alpha][beta]] - [[zeta].sup.[alpha][beta]], while its determinant is g = [g.sup.(0)(1 + [zeta]).

Correct linearization of Einstein's equations

Importantly, these are not considered to be indices that transform as co and contravariant tensors under the metric h.

Gauge freedom and relativity: a unified treatment of electromagnetism, gravity and the Dirac field