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