Bounds for the eigenvalues of block 2 × 2 Hermitian positive-definite matrices<FNR></FNR><FN>Dedicated to Owe Axelsson on the occasion of his 70th birthday. </FN>.

Lower and upper conditional bounds for the eigenvalues of a Hermitian positive-definite block 2 × 2 matrix, describing their closest possible location, are derived. The notions of partially and totally optimal spectra are introduced, and several equivalent characterizations of matrices with partially and totally optimal spectra are presented. It is shown that the block 2 × 2 block Jacobi scaled matrices and the so-called equilibrated matrices have totally optimal spectra. Copyright © 2005 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]