THE BLOCK LOWER BOUNDS FOR THE SMALLEST SINGULAR VALUE

1 Introduction and PreliminariesIt is well known that the smallest singular value of a matrix is important in matrixthoery and applications.Varah and Qi,Johnson gave some results on lower bound of thesmallest singular value1—4].Here,we use the block partitioned form of a matrix to ob-tain generalized lower bounds for σ_n(A).Furthermore,by scaling with a matrix D we ob-tain a new lower bound for σ_(A) of matrices which are not positive definite matrices.