Closest Matrices in the Space of Generalized Doubly Stochastic Matrices
Copyright policy )Closest Matrices in the Space of Generalized Doubly Stochastic Matrices
The author constructs the closest matrix \(B^*\) in \(\Omega_n\) (the collection of doubly stochastic \(n\times n\) real matrices) to a given real matrix \(A\) in \(M_n\) (the space of all \(n\times n\) real matrices). He also proves that \(B^* =(I_n-J_n) A(J_n-J_n) +J_n\), where \(J_n\) is \(n\times n\) real matrix the entries of which are all equal to \(1/n\) and \(I_n\) is \(n\times n\) real identity matrix in \(M_n\).
- University of Houston - Downtown United States
closest matrix, Applied Mathematics, Norms of matrices, numerical range, applications of functional analysis to matrix theory, doubly stochastic matrices, Analysis, Stochastic matrices
closest matrix, Applied Mathematics, Norms of matrices, numerical range, applications of functional analysis to matrix theory, doubly stochastic matrices, Analysis, Stochastic matrices
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