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Abstract:
Several neurological disorders can be described as alterations of the brain connectome, both anatomic and functional. To model diseases and compare them, it has been proposed the Krankheit-operator (K-operator), which acts on the weights of the connectome, reproducing the effects of specific disorders. In this article, with algebraic tools, we attempt to provide a more general definition of the operator, that encompasses the previous different definitions provided. We consider a general setting where the linear operator is an endomorphism on the vector space of n × n matrices. We show that the left and right matrix multiplication and a Hadamard multiplications can all be described as a special structured operator.
