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An [[Affine tensor|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.