The Nearest Generalized Doubly Stochastic Matrix to a Real Matrix with the same First and Second Moment
نویسندگان
چکیده
Let T be an arbitrary n × n matrix with real entries. We explicitly find the closest (in Frobenius norm) matrix A to T , where A is n × n with real entries, subject to the condition that A is “generalized doubly stochastic” (i.e. Ae = e and eA = e , where e = (1, 1, ..., 1) , although A is not necessarily nonnegative) and A has the same first moment as T (i.e. eT1 Ae1 = e T 1 Te1). We also explicitly find the closest matrix A to T when A is generalized doubly stochastic has the same first moment as T and the same second moment as T (i.e. eT1 A e1 = e T 1 T e1), when such a matrix A exists.
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