Abstract
The paper completely solves the problem of optimal diagonal scaling for quasireal Hermitian positive-definite matrices of order 3. In particular, in the most interesting irreducible case, it is demonstrated that for any matrix C from the class considered there is a uniquely determined optimally scaled matrix D0*CD0 of one of the four canonical types. Formulas for the entries of the diagonal matrix D0 are presented, as well as formulas for the eigenvalues and eigenvectors of D0*CD0 and for the optimal condition number of C, which is equal to k(D0*CD0). The optimality of the Jacobi scaling is analyzed. Bibliography: 10 titles.
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