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- W1965193630 abstract "Let Mn(F) denote the algebra of n×n matrices over the field F of complex, or real, numbers. Given a self-adjoint involution J∈Mn(C), that is, J=J*,J2=I, let us consider Cn endowed with the indefinite inner product [,] induced by J and defined by [x,y]≔〈Jx,y〉,x,y∈Cn. Assuming that (r,n-r), 0⩽r⩽n, is the inertia of J, without loss of generality we may assume J=diag(j1,⋯,jn)=Ir⊕-In-r. For T=(|tik|2)∈Mn(R), the matrices of the form T=(|tik|2jijk), with all line sums equal to 1, are called J-doubly stochastic matrices. In the particular case r∈{0,n}, these matrices reduce to doubly stochastic matrices, that is, non-negative real matrices with all line sums equal to 1. A generalization of Birkhoff’s theorem on doubly stochastic matrices is obtained for J-doubly stochastic matrices and an application to determinants is presented." @default.
- W1965193630 created "2016-06-24" @default.
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- W1965193630 date "2007-11-01" @default.
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- W1965193630 title "An extension of Birkhoff’s theorem with an application to determinants" @default.
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- W1965193630 doi "https://doi.org/10.1016/j.laa.2007.06.025" @default.
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