%0 Journal Article %1 johnson81 %A Johnson, Charles R. %A Robinson, Herbert A. %D 1981 %J Linear Algebra and its Applications %K eigenvalues matrix principal.submatrix %P 11--22 %R 10.1016/0024-3795(81)90163-4 %T Eigenvalue Inequalities for Principal Submatrices %V 37 %X For a polynomial with real roots, inequalities between those roots and the roots of the derivative are demonstrated and translated into eigenvalue inequalities for a hermitian matrix and its submatrices. For example, given an n-by-n positive definite hermitian matrix with maximum eigenvalue λ, these inequalities imply that some principal submatrix has an eigenvalue exceeding (n−1)nλ.

@article{johnson81, abstract = {For a polynomial with real roots, inequalities between those roots and the roots of the derivative are demonstrated and translated into eigenvalue inequalities for a hermitian matrix and its submatrices. For example, given an n-by-n positive definite hermitian matrix with maximum eigenvalue λ, these inequalities imply that some principal submatrix has an eigenvalue exceeding [(n−1)n]λ. }, added-at = {2017-02-01T07:52:47.000+0100}, author = {Johnson, Charles R. and Robinson, Herbert A.}, biburl = {https://www.bibsonomy.org/bibtex/295893c92862f4e7ffb5b51a42604447f/ytyoun}, doi = {10.1016/0024-3795(81)90163-4}, interhash = {b1153d66b72c98ec3de26ad416a7ba44}, intrahash = {95893c92862f4e7ffb5b51a42604447f}, issn = {0024-3795}, journal = {Linear Algebra and its Applications }, keywords = {eigenvalues matrix principal.submatrix}, pages = {11--22}, timestamp = {2017-02-01T07:52:47.000+0100}, title = {Eigenvalue Inequalities for Principal Submatrices }, volume = 37, year = 1981 }