Geodesic
Rational Tensor Representations of Hom(V, V) and an Extension of an Inequality of I. Schur.
Canadian journal of mathematics, Tome 24 (1972) no. 4, pp. 686-695

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Let V be an n-dimensional vector space over the complex numbers equipped with an inner product (x, y), and let (P, μ) be a symmetry class in the mth tensor product of V associated with a permutation group G and a character χ (see below). Then for each T ∊ Hom (V, V) the function φ which sends each m-tuple (v1, ... , vm) of elements of V to the tensor μ(TV1, ... , Tvm) is symmetric with respect to G and x, and so there is a unique linear map K(T) from P to P such that φ = K(T)μ.It is easily checked that K: Hom(V, V) → Hom(P, P) is a rational representation of the multiplicative semi-group in Hom(V, V): for any two linear operators S and T on V K(ST) = K(S)K(T).Moreover, if T is normal then, with respect to the inner product induced on P by the inner product on V (see below), K(T) is normal. 
Marcus, Marvin; Gordon, William Robert. Rational Tensor Representations of Hom(V, V) and an Extension of an Inequality of I. Schur.. Canadian journal of mathematics, Tome 24 (1972) no. 4, pp. 686-695. doi: 10.4153/CJM-1972-064-8
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