An affine tensor of type . Specifying an affinor with components is equivalent to specifying an endomorphism of the vector space according to the rule . To the identity endomorphism there corresponds a unique affinor. The correspondence by which the matrix 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.
I.e. one is concerned here with the isomorphism of linear algebra.
Affinor. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Affinor&oldid=17931