Geodesic
Linear Transformations on Matrices: The Invariance of a Class of General Matrix Functions
Canadian journal of mathematics, Tome 29 (1977) no. 5, pp. 937-946

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Let F be a field, F* be its multiplicative group and Mn (F) be the vector space of all n-square matrices over F. Let Sn be the symmetric group acting on the set {1, 2, ... , n}. If G is a subgroup of Sn and λ is a function on G with values in F, then the matrix function associated with G and X, denoted by G λ, is defined by and letI(G, λ) = { T : T is a linear transformation of Mn (F) to itself and G λ(T(X)) = G λ(X) for all X}. 
Ong, Hock. Linear Transformations on Matrices: The Invariance of a Class of General Matrix Functions. Canadian journal of mathematics, Tome 29 (1977) no. 5, pp. 937-946. doi: 10.4153/CJM-1977-094-4
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