MORE ESTIMATES FOR EIGENVALUES AND SINGULAR-VALUES

There is an interesting relation between the angle that a matrix forms with the identity and its eigenvalues. Then we show, for symmetric matrices, that some information about the matrixcan be known if the angle is computed. A lower bound for the maximum eigenvalue is obtained for symmetric positive semidefinite matrices; this inequality and the upper bound for eigenvalues given in [5] provide us an interval in which must lie the maximum eigenvalue. Finally some results from [5] and the first part of this paper are generalized for the non-symmetric case.