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Linear Transformations on Matrices: The Invariance of a Class of General Matrix Functions
Published online by Cambridge University Press: 20 November 2018
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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 Gλ, is defined by
and let
ℐ(G, λ) = { T : T is a linear transformation of Mn(F) to itself and Gλ(T(X)) = Gλ(X) for all X}.
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- Copyright © Canadian Mathematical Society 1977