Affinor

An affine tensor of type $ (1, 1) $. Specifying an affinor with components $ f _ {j} ^ { i } $ is equivalent to specifying an endomorphism of the vector space according to the rule $ v ^ {i} = f _ {s} ^ { i } v ^ {s} $. To the identity endomorphism there corresponds a unique affinor. The correspondence by which the matrix $ | f _ {j} ^ { i } | $ is assigned to each affinor realizes an isomorphism between the algebra of affinors and the algebra of matrices. An affinor is sometimes defined in the literature as a general (affine) tensor.

Comments

I.e. one is concerned here with the isomorphism $ V^\star \otimes V \simeq \mathop{\rm End} ( V ) $ of linear algebra.